Explore the vast range of titles available.

Micro‐continuum models are versatile and powerful approaches for simulating coupled processes in two‐scale porous systems. Initially oriented for modeling static single‐phase flow in microtomography images with sub‐voxel porosity, the concept has been extended over the years to multi‐phase flow, reactive transport, and poromechanics. This paper introduces an integrated micro‐continuum framework to model coupled processes in porous media. It reviews state‐of‐the‐art models and discusses applications in geosciences including Digital Rock Physics with sub‐voxel porosity, moving fluid‐solid interface at the pore‐scale due to geochemical reactions, fracture‐matrix interactions, and solid deformation. Finally, the paper discusses future developments in micro‐continuum models. Key Points Micro‐continuum models are hybrid‐scale approaches for solving flow and transport in porous media State of the art micro‐continuum models handle full Temperature‐Hydrodynamics‐Mechanics‐Chemistry coupling in unsaturated environments Applications include Digital Rock Physics with sub‐voxel porosity, pore‐scale reactive transport, and poromechanics

Fluid–mineral and fluid–rock interfaces are key parameters controlling the reactivity and fate of fluids in reservoir rocks and aquifers. The interface dynamics through space and time results from complex processes involving a tight coupling between chemical reactions and transport of species as well as a strong dependence on the physical, chemical, mineralogical and structural properties of the reacting solid phases. In this article, we review the recent advances in pore-scale imaging and reactive flow modelling applied to interface dynamics. Digital rocks derived from time-lapse X-ray micro-tomography imaging gives unprecedented opportunity to track the interface evolution during reactive flow experiments in porous or fractured media, and evaluate locally mineral reactivity. The recent improvements in pore-scale reactive transport modelling allow for a fine description of flow and transport that integrates moving fluid–mineral interfaces inherent to chemical reactions. Combined with three-dimensional digital images, pore-scale reactive transport modelling complements and augments laboratory experiments. The most advanced multi-scale models integrate sub-voxel porosity and processes which relate to imaging instrument resolution and improve upscaling possibilities. Two example applications based on the solver porousMedia4Foam illustrate the dynamics of the interface for different transport regimes (i.e., diffusive- to advective-dominant) and rock matrix properties (i.e., permeable vs. impermeable, and homogeneous vs. polymineralic). These parameters affect both the interface roughness and its geometry evolution, from sharp front to smeared (i.e., diffuse) interface. The paper concludes by discussing the challenges associated with precipitation processes in porous media, rock texture and composition (i.e., physical and mineralogical heterogeneity), and upscaling to larger scales.

The fluid‐flow properties of fractures have received increasing attention regarding the role of geofluids in the genesis of slow and fast earthquakes and recent advances in geoengineering developments. Geophysical observations are promising tools to remotely estimate crustal permeability changes; however, quantitative interpretations are limited by the rock‐physical models' paucity for fractures. This study investigated changes in permeability, resistivity, and their respective relationships at elevated stress by performing numerical simulations of different fracture models with varying fracture size, roughness, and shear displacement. Numerical results and microscopic flow analysis demonstrate that permeability–resistivity relationships are controlled by percolation and are less dependent on fracture geometric characteristics. Our finding suggests that the permeability evolution of fractures can be formulated with resistivity changes independent of both fracture size and microstructure, the trends of which can be predicted using Archie's exponent. The extension to the electro‐mechanical relationship further derives the potential applications of estimating stress changes. Plain Language Summary Monitoring the flow of fluids through underground fractures is important for developing earth resources and understanding the generation of both slow and fast earthquakes. This can be realized by observing physical properties underground such as electrical resistivity; however, the relationships between electrical and hydraulic properties are poorly understood because we have limited data on rock fractures. Thus, in this study, we explored changes in the hydraulic and electrical properties of synthetic rock fractures by subjecting them to increasing normal stress and shear displacement while varying the properties of the fracture surface topographies and length scales referring to natural data. We formulated the relationship between electrical resistivity and permeability invariant of fracture size, roughness, shear displacement, and normal stress based on both the theoretical model and empirical Archie's equation. We found that the rigorous relationship is controlled by the local connection of the fluid‐flow paths based on the microscopic flow analysis. The proposed formula can estimate the permeability evolution of fractures using resistivity data and is a better approach compared to porosity estimation because resistivity–porosity relationship can change depending on the tortuosity or connectivity. The extension to the electro‐mechanical relationship also derives the potential applications of estimating changes in pore pressure. Key Points Numerical results clarify the dependencies of fracture size, roughness, shear displacement, and stress on permeability and resistivity Flow path percolation can be correlated with tortuosity, which controls the rigorous resistivity–porosity and –permeability relationships Archie's exponent is constant for a percolated single fracture and can be used for monitoring permeability and pore pressure change

Image segmentation remains the most critical step in Digital Rock Physics (DRP) workflows, affecting the analysis of physical rock properties. Conventional segmentation techniques struggle with numerous image artifacts and user bias, which lead to considerable uncertainty. This study evaluates the advantages of using the random forest (RF) algorithm for the segmentation of fractured rocks. The segmentation quality is discussed and compared with two conventional image processing methods (thresholding-based and watershed algorithm) and an encoder–decoder network in the form of convolutional neural networks (CNNs). The segmented images of the RF method were used as the ground truth for CNN training. The images of two fractured rock samples are acquired by X-ray computed tomography scanning (XCT). The skeletonized 3D images are calculated, providing information about the mean mechanical aperture and roughness. The porosity, permeability, flow fields, and preferred flow paths of segmented images are analyzed by the DRP approach. Moreover, the breakthrough curves obtained from tracer injection experiments are used as ground truth to evaluate the segmentation quality of each method. The results show that the conventional methods overestimate the fracture aperture. Both machine learning approaches show promising segmentation results and handle all artifacts and complexities without any prior CT-image filtering. However, the RF implementation has superior inherent advantages over CNN. This method is resource-saving (e.g., quickly trained), does not need an extensive training dataset, and can provide the segmentation uncertainty as a measure for evaluating the segmentation quality. The considerable variation in computed rock properties highlights the importance of choosing an appropriate segmentation method.

Understanding two‐phase flow in laminated sandstones is important for fluid migration control and operational strategy determination in underground energy and hydrology engineering projects. Digital core analysis provides unparalleled understanding of two‐phase flow in complex porous media, but the integration into field analytical workflow is obstructed by the huge computational burden and imaging limitations on a standard rock core. To address this challenge, we propose a novel pore‐scale rock‐typing and upscaling approach for fast computation of two‐phase flow properties on large three‐dimensional digital rock images that contain billions of voxels. Firstly, a heterogeneous rock sample is divided into several homogeneous rock types through data clustering of regional 3D morphological parameters, and their two‐phase flow properties are calculated from selected subsamples using in‐house pore‐network model. The capillary pressure and relative permeability curves of the full digital image are then estimated through quasi‐static modeling on the rock type distribution. The excellent agreement between the upscaling results and pore‐scale simulations on the full image has verified the effectiveness of this two‐phase flow upscaling strategy. With largely reduced computational demands and clearly defined lamination heterogeneity, this approach has demonstrated good potential in bridging the gap between pore‐scale and core‐scale fluid flow mechanisms. In addition, due to the laminated structural characteristics, we also find a significant reduction in phase mobility over a range of saturations in the relative permeability curves of this highly permeable rock sample.

The morphology of fault zones formed by slow faulting is markedly different from that of brittle faulting. In this study, we quantify the three‐dimensional (3D) pore distribution and permeability structures of two rock samples that have been deformed to failure by slow and brittle faulting, respectively. Our results show that the permeability structure of fault zones varies greatly depending on the faulting mechanism. Fault cores formed by slow faulting exhibit much higher porosity and permeability compared to the surrounding damage zone and wall rocks, unlike those formed through brittle faulting. Since slow slip events associated with high pore fluid pressures are common in active tectonic regions, we propose that slow slip events can serve as a mechanism to maintain the permeable pathways beneath the seismogenic zone, facilitating the movement of mantle‐derived fluids from deep reservoirs toward the surface.

Predicting the petrophysical properties of rock samples using micro-CT images has gained significant attention recently. However, an accurate and an efficient numerical tool is still lacking. After investigating three numerical techniques, (i) pore network modeling (PNM), (ii) the finite volume method (FVM), and (iii) the lattice Boltzmann method (LBM), a workflow based on machine learning is established for fast and accurate prediction of permeability directly from 3D micro-CT images. We use more than 1100 samples scanned at high resolution and extract the relevant features from these samples for use in a supervised learning algorithm. The approach takes advantage of the efficient computation provided by PNM and the accuracy of the LBM to quickly and accurately estimate rock permeability. The relevant features derived from PNM and image analysis are fed into a supervised machine learning model and a deep neural network to compute the permeability in an end-to-end regression scheme. Within a supervised learning framework, machine and deep learning algorithms based on linear regression, gradient boosting, and physics-informed convolutional neural networks (CNNs) are applied to predict the petrophysical properties of porous rock from 3D micro-CT images. We have performed the sensitivity analysis on the feature importance, hyperparameters, and different learning algorithms to make a prediction. Values of R 2 scores up to 88% and 91% are achieved using machine learning regression models and the deep learning approach, respectively. Remarkably, a significant gain in computation time—approximately 3 orders of magnitude—is achieved by applied machine learning compared with the LBM. Finally, the study highlights the critical role played by feature engineering in predicting petrophysical properties using deep learning.

Estimating porosity and permeability for porous rock is a vital component of reservoir engineering, and imaging techniques have to date focused on methodologies to match image-derived flow parameters with experimentally identified values. Less emphasis has been placed on the trade-off between imaging complexity, computational time, and error in identifying porosity and permeability. Here, the effect of image resolution on the permeability derived from micro-X-ray microscopy (micro-XRM) is discussed. A minicore plug of Bentheimer sandstone is imaged at a resolution of 1024 × 1024 × 1024 voxels, with a voxel size of 1.53  μ m , and progressively rebinned to as low as 32 voxels per side (voxel size 48.96  μ m ). Pore-scale flow is modeled using the finite volume method in the open-source program OpenFOAM ® . A sharp drop in permeability between images with a voxel size of 24 and 12  μ m suggests that an optimal speed/resolution trade-off may be found. The primary source of error is due to reassignment of voxels along the pore–solid interface and the subsequent change in pore connectivity. We observe the error in permeability and porosity due to both image resolution and thresholding values in order to find a method that balances an acceptable error range with reasonable computation time.

The introduction of deep learning techniques has revolutionized the automated segmentation of digital rock images. These methods enable precise evaluations of critical properties such as porosity and fluid flow characteristics, thereby enhancing the efficiency of reservoir characterization. This study explores the application of state-of-the-art Convolutional Neural Network (CNN) architectures for analyzing rock micro-CT images, aiming to enhance reservoir characterization efficiency. Specifically, we implement various deep learning models, including Fully Convolutional Networks, Encoder-Decoder Models, Multi-Scale Networks, Dilated Convolution Models, and Attention-Based Models. The segmentation performance of these CNN architectures is benchmarked against the traditional Otsu thresholding method using a dataset of 5,000 2D slices of ten distinct sandstone types, each with a voxel resolution of 2.25 × 2.25 × 2.25 µm. Our evaluation utilizes pixel-wise accuracy metrics such as F1-score, binary-IOU, Recall, and Precision. To replicate the physics of pore-scale fluid movement, various numerical simulation methods such as the Lattice Boltzmann Method (LBM), Pore Network Modeling (PNM), and Computational Fluid Dynamics (CFD) are employed to predict the permeability and rock formation factor of a blind sample, using CNNs for image segmentation. Our findings reveal that advanced CNNs significantly outperform the Otsu method in both pixel-wise segmentation accuracy and fluid flow simulation performance. Among all CNNs, EfficientNetB0-Unet, VGG16-Unet, and Enet exhibit exceptional performance in segmenting complex pore structures, as evidenced by their high F1-scores and binary-IOU metrics as well as accurate predictions of porosity, permeability, and formation factor.

We present a memory-efficient algorithm for significantly enhancing the quality of segmented 3D micro-Computed Tomography (micro-CT) images of rocks using a Machine Learning (ML) Generative Model. The proposed model achieves a 16 × increase in resolution and corrects inaccuracies in segmentation caused by the overlapping X-ray attenuation in micro-CT measurements across different minerals. The generative model employed is a 3D Octree-Based Progressive Growing Deep Convolutional Wasserstein Generative Adversarial Network with Gradient Penalty (3D OB PG DC WGAN-GP). To address the challenge of extremely high memory consumption inherent in standard PyTorch 3D Convolutional (Conv3D) layers, which is a significant constraint in 3D Super-Resolution (SR) applications, we implemented an Octree structure within the 3D Progressive Growing Generator (3D PG G) model. This enabled the use of memory-efficient 3D Octree-Based Convolutional layers provided by the open-source Minkowski Engine library. The adoption of the octree structure was pivotal in overcoming the long-standing memory bottleneck in volumetric deep learning, making it possible to reach 16 × Super-Resolution in 3D, a scale that is challenging to attain due to cubic memory scaling. For training, we utilized segmented 3D Low-Resolution (LR) micro-CT images along with unpaired segmented complementary 2D High-Resolution (HR) Laser Scanning Microscope (LSM) images. Post-training, we achieved high-quality, segmented 3D SR images with resolutions improved from 7 to 0.44 µm/voxel and accurate segmentation of constituent minerals. Validated on Berea sandstone, this framework demonstrates substantial improvements in pore characterization and mineral differentiation, which are key factors for accurate Digital Rock Physics (DRP) simulations. The proposed algorithm advances the feasibility of large-scale, high-resolution 3D reconstructions and offers a robust solution to one of the primary computational limitations in modern geoscientific imaging.