We use Wasserstein Generative Adversarial Networks to learn and integrate multi-scale features in segmented three-dimensional images of porous materials, enabling the dependable generation of large-scale representations of complex porous media. A Laplacian pyramid generator is introduced which creates pore-space features with a hierarchy of spatial scales. Feature statistics mixing regularization enhances the ability of the model generation to reliably maintain multi-scale pore-space features of images by increasing diversity. The method is tested on a variety of X-ray images of porous rocks. The generated images can be of any size -- cm-scale ten-billion-cell images are generated to demonstrate the power of the approach -- which have two-point correlation functions, porosity, permeability, Euler characteristic, curvature, and specific surface area close to the training datasets. The images demonstrate a considerable improvement over previously- published studies using generative adversarial networks.

Porous materials, such as carbonate rocks, frequently have pore sizes which span many orders of magnitude. This is a challenge for models that rely on an image of the pore space, since much of the pore space may be unresolved. There is a trade off between image size and resolution. For most carbonates, to have an image sufficiently large to be representative of the pore structure, many fine details cannot be captured. In this work, sub-resolution porosity in X-ray images is characterized using differential imaging which quantifies the difference between a dry scan and 30 wt\% KI brine saturated rock images. Once characterized, we develop a robust workflow to incorporate the sub-resolution pore space into network model using Darcy-type elements called micro-links. Each grain voxel with sub-resolution porosity is assigned to the two nearest resolved pores using an automatic dilation algorithm. By including these micro-links with empirical models in flow modeling, we simulate single-phase and multiphase flow. By fine-tuning the micro-link empirical models, we achieve effective permeability, formation factor, and drainage capillary pressure predictions that align with experimental results. We then show that our model can successfully predict steady-state relative permeability measurements on a water-wet Estaillades carbonate sample within the uncertainty of the experiments and modeling. Our approach of incorporating sub-resolution porosity in two-phase flow modeling using image-based multiscale pore network techniques can capture complex pore structures and accurately predict flow behavior in porous materials with a wide range of pore size.

We use fast synchrotron X-ray imaging to understand three-phase flow in mixed-wet porous media to design either enhanced permeability or capillary trapping. The dynamics of these phenomena are of key importance in subsurface hydrology, carbon dioxide storage, oil recovery, food and drug manufacturing, and chemical reactors. We study the dynamics of a water-gas-water injection sequence in a mixed-wet carbonate rock. During the initial waterflooding, water displaced oil from pores of all size, indicating a mixed-wet system with local contact angles both above and below 90 •. When gas was injected, gas displaced oil preferentially with negligible displacement of water. This behaviour is explained in terms of the gas pressure needed for invasion. Overall, gas behaved as the most non-wetting phase with oil the most wetting phase; however pores of all size were occupied by oil, water and gas, as a signature of mixed-wet media. Thick oil wetting layers were observed, which increased oil connectivity and facilitated its flow during gas injection. A chase waterflooding resulted in additional oil flow, while gas was trapped by oil and water. Furthermore, we quantified the evolution of the surface areas and both Gaussian and the total curvature, from which capillary pressure could be estimated. These quantities are related to the Minkowski functionals which quantify the degree of connectivity and trapping. The combination of water and gas injection, under mixed-wet immiscible conditions leads to both favourable oil flow, but also to significant trapping of gas, which is advantageous for storage applications.