Ying Da Wang

Arash Rabbani, Masoud Babaei, Reza Shams et al.

DeePore is a deep learning workflow for rapid estimation of a wide range of porous material properties based on the binarized micro-tomography images. By combining naturally occurring porous textures we generated 17700 semi-real 3-D micro-structures of porous geo-materials with size of 256^3 voxels and 30 physical properties of each sample are calculated using physical simulations on the corresponding pore network models. Next, a designed feed-forward convolutional neural network (CNN) is trained based on the dataset to estimate several morphological, hydraulic, electrical, and mechanical characteristics of the porous material in a fraction of a second. In order to fine-tune the CNN design, we tested 9 different training scenarios and selected the one with the highest average coefficient of determination (R^2) equal to 0.885 for 1418 testing samples. Additionally, 3 independent synthetic images as well as 3 realistic tomography images have been tested using the proposed method and results are compared with pore network modelling and experimental data, respectively. Tested absolute permeabilities had around 13 % relative error compared to the experimental data which is noticeable considering the accuracy of the direct numerical simulation methods such as Lattice Boltzmann and Finite Volume. The workflow is compatible with any physical size of the images due to its dimensionless approach and can be used to characterize large-scale 3-D images by averaging the model outputs for a sliding window that scans the whole geometry.

Ying Da Wang, Traiwit Chung, Ryan T. Armstrong et al.

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.

Ying Da Wang, Mehdi Shabaninejad, Ryan T. Armstrong et al.

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 $μ$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.

Ying Da Wang, Ryan T. Armstrong, Peyman Mostaghimi

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.

Ying Da Wang, Ryan Armstrong, Peyman Mostaghimi

Single Image Super Resolution (SISR) techniques based on Super Resolution Convolutional Neural Networks (SRCNN) are applied to micro-computed tomography (μCT) 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.