Complex flow dynamics have been observed, at the pore-scale, during multiphase through porous rocks. These dynamics are not captured in large scale models exploring the migration and trapping of subsurface fluids e.g., CO2 or hydrogen. Due to limitations in imaging capabilities, these dynamics cannot be observed directly at the larger, Darcy scale. Instead, by using pressure data from pore-scale (mm-scale) and core-scale (cm-scale) experiments, we show that fluctuations in pressure measured at the core-scale reflect specific fluid displacement events taking place at the pore-scale. The spectral characteristics of the pressure data depends on the flow dynamics, size of the rock sample, and heterogeneity of pore space. While high resolution imaging of large samples would be useful in assessing flow dynamics across many of the scales of interest, such an approach is currently infeasible. We suggest an alternative, pragmatic, approach examining pressure data in the time-frequency domain using wavelet transformation.

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.

Many subsurface fluid flows, including the storage of CO underground or the production of oil, are transient processes incorporating multiple fluid phases. The fluids are not in equilibrium meaning macroscopic properties such as fluid saturation and pressure vary in space and time. However, these flows are traditionally modelled with equilibrium (or steady-state) flow properties, under the assumption that the pore scale fluid dynamics are equivalent. In this work, we used fast synchrotron X-ray tomography with 1s time resolution to image the pore scale fluid dynamics as the macroscopic flow transitioned to steady-state. For nitrogen or decane, and brine injected simultaneously into a porous rock we observed distinct pore scale fluid dynamics during transient flow. Transient flow was found to be characterised by intermittent fluid occupancy, whereby flow pathways through the pore space were constantly rearranging. The intermittent fluid occupancy was largest and most frequent when a fluid initially invaded the rock. But as the fluids established an equilibrium the dynamics decreased to either static interfaces between the fluids or small-scale intermittent flow pathways, depending on the capillary number and viscosity ratio. If the fluids were perturbed after an equilibrium was established, by changing the flow rate, the transition to a new equilibrium was quicker than the initial transition. Our observations suggest that transient flows require separate modelling parameters. The timescales required to achieve equilibrium suggest that several metres of an invading plume front will have flow properties controlled by transient pore scale fluid dynamics.

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.