Mechanisms controlling fluid breakup and reconnection during two-phase flow in porous media

A Statistical Analysis of Fluid Interface Fluctuations: Exploring the Role of Viscosity Ratio

Understanding multiphase flow through porous media is integral to geologic carbon storage or hydrogen storage. The current modelling framework assumes each fluid present in the subsurface flows in its own continuously connected pathway. The restriction in flow caused by the presence of another fluid is modelled using relative permeability functions. However, dynamic fluid interfaces have been observed in experimental data, and these are not accounted for in relative permeability functions. In this work, we explore the occurrence of fluid fluctuations in the context of sizes, locations, and frequencies by altering the viscosity ratio for two-phase flow. We see that the fluctuations alter the connectivity of the fluid phases, which, in turn, influences the relative permeability of the fluid phases present.

Reconstructing high fidelity digital rock images using deep convolutional neural networks

Imaging methods have broad applications in geosciences. Scanning electron microscopy (SEM) and micro-CT scanning have been applied for studying various geological problems. Despite significant advances in imaging capabilities, and image processing algorithms, acquiring high-quality data from images is still challenging and time-consuming. Obtaining a 3D representative volume for a tight rock sample takes days to weeks. Image artifacts such as noise further complicate the use of imaging methods for the determination of rock properties. In this study, we present applications of several convolutional neural networks (CNN) for rapid image denoising, deblurring and super-resolving digital rock images. Such an approach enables rapid imaging of larger samples, which in turn improves the statistical relevance of the subsequent analysis. We demonstrate the application of several CNNs for image restoration applicable to scientific imaging. The results show that images can be denoised without a priori knowledge of the noise with great confidence. Furthermore, we show how attaching several CNNs in an end-to-end fashion can improve the final quality of reconstruction. Our experiments with SEM and CT scan images of several rock types show image denoising, deblurring and super-resolution can be performed simultaneously.

Dynamic fluid configurations in steady-state two-phase flow in Bentheimer sandstone

Fast synchrotron tomography is used to study the impact of capillary number, Ca, on fluid configurations in steady-state two-phase flow in porous media. Brine and n-decane were co-injected at fixed fractional flow, f_{w}=0.5, in a cylindrical Bentheimer sandstone sample for a range of capillary numbers 2.1×10^{-7}≤Ca≤4.2×10^{-5}, while monitoring the pressure differential. As we have demonstrated in Gao et al. [Phys. Rev. Fluids 5, 013801 (2020)2469-990X10.1103/PhysRevFluids.5.013801], dependent on Ca, different flow regimes have been identified: at low Ca only fixed flow pathways exist, while after a certain threshold dynamic effects are observed resulting in intermittent fluctuations in fluid distribution which alter fluid connectivity. Additionally, the flow paths, for each capillary number, were imaged multiple times to quantify the less frequent changes in fluid occupancy, happening over timescales longer than the duration of our scans (40 s). In this paper we demonstrate how dynamic connectivity results from the interaction between oil ganglia populations. At low Ca connected pathways of ganglia are fixed with time-independent small, medium, and large ganglia populations. However, with an increase in Ca we see fluctuations in the size and numbers of the larger ganglia. With the onset of intermittency, fluctuations occur mainly in pores and throats of intermediate size. When Ca is further increased, we see rapid changes in occupancy in pores of all size. By combining observations on pressure fluctuations and flow regimes at various capillary numbers, we summarize a phase diagram over a range of capillary numbers for the wetting and nonwetting phases, Ca_{w} and Ca_{nw}, respectively, to quantify the degree of intermittent flow. These different regimes are controlled by a competition between viscous forces on the flowing fluids and the capillary forces acting in the complex pore space. Furthermore, we plot the phase diagrams of the transition from Darcy flow to intermittent flow over a range of Reynolds and Weber numbers for the wetting and nonwetting phases to evaluate the balance among capillary, viscous, and inertial forces, incorporating data from the literature. We demonstrate that pore geometry has a significant control on flow regime.

Upscaling the porosity-permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning

The permeability of a pore structure is typically described by stochastic representations of its geometrical attributes (e.g. pore-size distribution, porosity, coordination number). Database-driven numerical solvers for large model domains can only accurately predict large-scale flow behavior when they incorporate upscaled descriptions of that structure. The upscaling is particularly challenging for rocks with multimodal porosity structures such as carbonates, where several different type of structures (e.g. micro-porosity, cavities, fractures) are interacting. It is the connectivity both within and between these fundamentally different structures that ultimately controls the porosity–permeability relationship at the larger length scales. Recent advances in machine learning techniques combined with both numerical modelling and informed structural analysis have allowed us to probe the relationship between structure and permeability much more deeply. We have used this integrated approach to tackle the challenge of upscaling multimodal and multiscale porous media. We present a novel method for upscaling multimodal porosity–permeability relationships using machine learning based multivariate structural regression. A micro-CT image of Estaillades limestone was divided into small 60³ and 120³ sub-volumes and permeability was computed using the Darcy–Brinkman–Stokes (DBS) model. The microporosity–porosity–permeability relationship from Menke et al. (Earth Arxiv, https://doi.org/10.31223/osf.io/ubg6p, 2019) was used to assign permeability values to the cells containing microporosity. Structural attributes (porosity, phase connectivity, volume fraction, etc.) of each sub-volume were extracted using image analysis tools and then regressed against the solved DBS permeability using an Extra-Trees regression model to derive an upscaled porosity–permeability relationship. Ten test cases of 360³ voxels were then modeled using Darcy-scale flow with this machine learning predicted upscaled porosity–permeability relationship and benchmarked against full DBS simulations, a numerically upscaled Darcy flow model, and a Kozeny–Carman model. All numerical simulations were performed using GeoChemFoam, our in-house open source pore-scale simulator based on OpenFOAM. We found good agreement between the full DBS simulations and both the numerical and machine learning upscaled models, with the machine learning model being 80 times less computationally expensive. The Kozeny–Carman model was a poor predictor of upscaled permeability in all cases.