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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Pore-Scale Simulation of Spectral Induced Polarization

A new model was developed to simulate spectral induced polarization (SIP) in porous media. The model is based on a pore-network approximation of the soil or rock, in which bonds between pores are represented by equivalent circuits. In the circuit model, electrolytic and surface conduction occur in parallel, with the electrolyte behaving as a single resistor, and the mineral surface behaving as a resistor and capacitor in series. Based on the pore geometry, fluid conductivity, and mineral surface conductivity, an impedance network is generated. SIP spectra are calculated by solving the sinusoidal steady-state electrical problem for a range of frequencies. The new model provides a tool to bridge the gap between (1) our fundamental understanding of polarization processes at the scale of a single pore or grains and (2) existing simulation capabilities for macroscale systems that do not account for pore-scale properties. The model is implemented in Matlab and can solve two-dimensional and three-dimensional (2D and 3D) networks. Examples for regular cubic lattices are presented, but the method and code are flexible with respect to pore geometries and allow for future leveraging of existing open-source capabilities for generation of pore networks and extraction of network geometries from micro imaging of core samples.

58 GEOSCIENCES↗
DOE OSTI2025

Computational Modeling of Molten Salt Infiltration and Oxidation in Nuclear Graphite

Graphite is utilized as a moderator and reflector in advanced nuclear reactor designs due to its high thermal conductivity, neutron moderation properties, and resistance to radiation damage. However, its longterm performance and reliability are challenged by degradation mechanisms such as molten salt infiltration in molten salt reactors (MSRs) and oxidation in gas-cooled reactors (GCRs). These mechanisms can compromise the structural integrity and operational lifetime of graphite components, necessitating a more detailed assessment of their physical behavior. This report focuses on the development of computational models for molten salt infiltration and oxidation of graphite to aid the design and performance analysis of graphite components. For molten salt infiltration, a computational framework is developed that couples incompressible Navier-Stokes and phase-field model to simulate the penetration of molten salt into graphite?s interconnected pore structure. Initial model verification is performed using two-phase flows in two dimensions, demonstrating the models ability to capture fundamental physical behavior and agree with analytical solution. This framework is then applied to a realistic IG110 nuclear graphite , where a computed tomography extracted pore geometry is used to analyse the infiltration behavior of FLiNaK molten salt. This model provides insights into how the microstructure and other relevant parameters influence the transport pathways of molten salt into graphite, potentially offering a means to rapidly evaluate a graphite grade?s resistance to infiltration. For oxidation, the report details pore-scale mass and heat transport models, describing the diffusion of gases, reaction kinetics, and thermal effects. Additionally, this report highlights inconsistencies in the existing volume-averaged macroscopic model, particularly in upscaling of reaction kinetics and flux terms, and surface to volume transformations. These inconsistencies suggest that current formulations may not accurately capture the experimentally observed graphite oxidation process, highlighting the need for improved model development. This work advances the development of physics-based computational models for graphite degradation, contributing to improved predictive models for next-generation nuclear reactor designs. Future efforts will focus on refining the infiltration model to address non-physical behaviors and enhance its robustness. Additionally, for oxidation, further studies will employ the principles of volume averaging to rigorously derive the upscaled equations, potentially in collaboration with subject matter experts.

Computational Modeling of Molten Salt Infiltration↗
DOE OSTI2024

Pore-scale visualization of natural hydrate-bearing sediments

Accurate modeling of gas hydrate reservoir productivity and geomechanical risks associated with subsurface dissociation of natural gas hydrates (NGH) requires the determination of model parameters through physical testing on natural hydrate-bearing sediments (HBS). This involves investigating the hydro-mechanical behavior of undisturbed hydrate samples from nature under in situ conditions using pressure core characterization and analysis, which provides a unique opportunity for research. By employing state-of-the-art micro computed tomography imagery on cryogenically preserved, hydrate-bearing sediment samples, we can determine hydrate saturation as well as permeability with and without the presence of hydrates in the sediment. Furthermore, utilizing a machine learning based image segmentation technique, it is possible to extract pore space and grain information. Subsections of the entire image volume were used to determine anisotropic permeabilities using a finite-difference method Stokes solver (FDMSS). Additionally, permeability measurements on whole pressure and temperature preserved hydrate-bearing core were analyzed by utilizing the National Energy Technology Laboratory’s (NETL) Pressure Core Characterization and X-ray CT Visualization Tool (PCXT) to manipulate, cut, and analyze pressure preserved sediment. Permeabilities were measured under a broad range of vertical stress states to simulate expected pressure changes during production scenarios, and the results show that permeabilities derived from images are in agreement with those from traditional core derived experiments. The collected stress-dependent permeability, permeability anisotropy, and corresponding gas hydrate saturations provide valuable input into numerical simulations of reservoir productivity. These properties have been proven to be key parameters determining a long-term reservoir response under depressurization.

Liu, Mengwei [Oak Ridge Institute for Science and ↗
DOE OSTI2024

The Method of Finite Averages: A rigorous upscaling methodology for heterogeneous porous media

Rigorous upscaling techniques offer accurate and computationally-efficient strategies for modeling the average behaviors of multi-physical, multiscale phenomena in geological porous media. However, such techniques often rely on a variety of methodological assumptions that prohibit their rigorous application to practical systems (e.g., systems involving heterogeneous porous media, system-scale boundary conditions, and fine-scale dynamics that are not diffusion-dominant). In this work, we aim to formulate an upscaling methodology with few methodological assumptions to provide high levels of model generality and foster the utilization of rigorously-derived upscaled models in practice. In particular, we introduce the Method of Finite Averages (MoFA), a novel upscaling methodology for rigorously modeling heterogeneous porous media and system-scale boundary conditions. We then detail MoFA’s implementation for the advective–diffusive transport of a single species and compare the methodology with classic numerical techniques, as well as other rigorous upscaling techniques, to highlight MoFA’s unique combination of rigor and generality. We then validate the derived model while demonstrating its benefits in three numerical experiments. The results suggest that (1.) the applicability and a priori error guarantees of MoFA models do not directly depend on system geometry, (2.) a model’s applicability and error guarantees can be can arbitrarily expanded and reduced, respectively, with further computational expense, and (3.) downscaling with MoFA provides an efficient strategy for generating accurate pore-scale solutions from upscaled results. Ultimately, the results evidence that upscaled models can be rigorously derived for heterogeneous porous media systems and resolved in a fraction of the time it takes to perform the equivalent pore-scale simulations.

58 GEOSCIENCES↗
DOE OSTI2025

Geochemical Assessment for Carbon Sequestration in the Conasauga Group, Northwest Georgia, USA

Sedimentary geological formations are known to be great candidates for geological carbon sequestration. Published studies suggest the southeast of the United States contains many formations suitable for carbon storage. The Cassville 1 Stratigraphic Borehole well could act as a potential carbon reservoir for nearby energy resource facilities in Georgia, United States. Although studies have shown that porous formations are adequate for geological carbon sequestration, it is important to understand possible geochemical reactions between CO 2 and the targeted geological formation before injecting any fluids. In this study, a sandstone sample from the Cassville 1 well is being considered for geological carbon sequestration in the Conasauga Group in Northwest Georgia. Here, the collected sandstone sample, consisting of quartz, K-feldspar, micas, kaolinite, and carbonate minerals such as calcite and dolomite, has a 6% porosity. Leveraging the formation composition and porosity, a one-dimensional continuum reactive transport model was built using CrunchFlow to assess possible geochemical reactions between injected CO 2 and the geological formation. Simulation results show that the carbonate minerals, calcite and dolomite, dissolve during the injection period of 10,000 days, increasing formation porosity from 6% to as much as 30%. The rate and extent of carbonate mineral dissolution and resulting porosity increase are highly sensitive to mineral reactive surface area values. No evidence of mineral precipitation was observed, suggesting that dissolution reactions will control porosity evolution during the CO 2 injection period.

42 ENGINEERING↗
DOE OSTI2023

A data-driven framework for permeability prediction of natural porous rocks via microstructural characterization and pore-scale simulation

Understanding the microstructure–property relationships of porous media is of great practical significance, based on which macroscopic physical properties can be directly derived from measurable microstructural informatics. However, establishing reliable microstructure–property mappings in an explicit manner is difficult, due to the intricacy, stochasticity, and heterogeneity of porous microstructures. In this paper, a data-driven computational framework is presented to investigate the inherent microstructure–permeability linkage for natural porous rocks, where multiple techniques are integrated together, including microscopy imaging, stochastic reconstruction, microstructural characterization, pore-scale simulation, feature selection, and data-driven modeling. A large number of 3D digital rocks with a wide porosity range are acquired from microscopy imaging and stochastic reconstruction techniques. A broad variety of morphological descriptors are used to quantitatively characterize pore microstructures from different perspectives, and they compose the raw feature pool for feature selection. Here high-fidelity lattice Boltzmann simulations are conducted to resolve fluid flow passing through porous media, from which reliable permeability references are obtained. The optimal feature set that best represents permeability is identified through a performance-oriented feature selection process, upon which a cost-effective surrogate model is rapidly fitted to approximate the microstructure-permeability mapping via data-driven modeling. This surrogate model exhibits great advantages over empirical/analytical formulas in terms of prediction accuracy and generalization capacity, which can predict reliable permeability values spanning four orders of magnitude. Besides, feature selection also greatly enhances the interpretability of the data-driven prediction model, from which new insights into the mechanism of how microstructural characteristics determine intrinsic permeability are obtained.

58 GEOSCIENCES↗
DOE OSTI2023

Modeling the 4D discharge of lithium-ion batteries with a multiscale time-dependent deep learning framework

The lithium-ion battery (LIB) field is moving towards the direction of investigating spatially resolved physical phenomena in the 3D porous microstructure of electrodes. These pore-scale simulations give new insights into the local dynamics of lithiation/de-lithiation and charge transport, Nevertheless, the computational time of these simulations limits the integration of these models in optimization workflows of cycling conditions or electrode manufacturing processes. Machine learning models present a way of assessing in real-time the performance of materials. While several successful techniques for replicating simulations with machine learning have been proposed, this case study presents a more demanding problem, due to the necessity of understanding the behavior of heterogeneous 3D local data, as it evolves in time: this poses both a scientific and a technical challenge. To this end, we propose an autoregressive multiscale convolutional neural network model to predict relevant quantities at the pore-scale in the solid phase: the lithium concentration (in the active material) and potential (in the active material and carbon binder). Here, these are ultimately used to reconstruct the battery discharge curve. 3D images of the electrode microstructures are the input to the network, trained with a dataset of finite element method simulations to predict the discharge behavior of the cathode side in lithium ion batteries. We propose this machine learning model as a proof-of-concept of the applicability of multiscale networks for time-dependent physics problems. The trained model exhibits very high accuracy (with errors lower than 2 %) in forecasting the discharge behavior of new unseen cathodes.

25 ENERGY STORAGE↗
DOE OSTI2025

The rigorous upscaling of advection-dominated transport in heterogeneous porous media via the Method of Finite Averages

Systems involving advection-dominated transport through heterogeneous porous and fractured media are ubiquitous in subsurface engineering applications. However, upscaling such systems continues to challenge rigorous modeling efforts, particularly when advection is stronger than diffusion at fine spatial scales (i.e., when the Péclet number is greater than one at length scales that characterize a system’s unit-cells, representative elementary volumes, or averaging regions). Here, in this work, we propose and validate a strategy for extending the Method of Finite Averages (MoFA), a rigorous upscaling methodology for heterogeneous porous media, to upscale transport systems experiencing stronger advection than diffusion at fine scales (i.e., fine-scale Péclet numbers greater than one). We detail the strategy, the physical conditions under which it can be applied while retaining a priori modeling error guarantees, and implement the strategy to obtain a MoFA model for advective-diffusive transport that accommodates advective physics at fine spatial scales. We then perform two numerical experiments considering systems with system-scale Péclet numbers of 300 and 1000 — which correspond to fine-scale Péclet numbers of 30 and 100, respectively — to verify that the error guarantees are met under the strategy. After, we conduct a numerical study to demonstrate the strategy’s advantages over the original MoFA methodology. The results suggest that rigorously-upscaled transport models for heterogeneous porous media experiencing advective physics at finer spatial scales can be derived through MoFA and resolved orders of magnitude faster than their pore-scale counterparts. The results also suggest that the presented strategy is limited to modeling shallow concentration gradients when there are large differences between the time scales related to advection and a system’s temporally-varying boundary conditions. This limitation hinders the strategy’s practicality in modeling more advective systems, and as such, opportunity exists for developing additional strategies that accommodate rapidly-varying boundary conditions — and consequentially, steeper concentration gradients — while modeling advective systems with MoFA.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Impact of Rock Wettability and Mineralization on CO 2 Storage Efficiency in Basalt Reservoirs

Basalt formations have emerged as highly promising targets for geological CO 2 storage due to their abundance of reactive silicate minerals that can rapidly convert dissolved CO 2 into stable carbonate minerals. The efficiency of CO 2 trapping in basalts, however, depends not only on their geochemical reactivity but also on reservoir wettability, which governs how CO 2 partitions among structural, residual, solubility, and mineral trapping mechanisms. However, wettability and mineral kinetics have largely been examined separately, wettability for plume migration and kinetics in terms of mineralization, leaving their coupled impact unquantified. Here, we systematically integrate th ese processes in a reservoir-scale reactive transport model to quantify the impact of three distinct wettability conditions (water-wet, mixed-wet, and CO 2 -wet) on plume migration, mineral precipitation, pore-scale blockage, and long-term immobilization. Results show that under ideal conditions (no mineralization), water-wet systems exhibited plume aspect ratios up to 28% higher than CO 2 -wet systems and promoted at least 60% greater residual trapping. When mineralization was incorporated, mineral trapping accounted for 57%, 53%, and 46% of the total immobilized CO 2 in water-wet, mixed-wet, and CO 2 -wet systems, respectively. Dissolved CO 2 contributed 43-46%, while residual trapping remained below 5%, and mobile CO 2 was substantially reduced due to mineralization, demonstrating that as the system becomes more water-wet, CO 2 is more effectively converted into stable carbonate minerals, although extensive mineral precipitation may lead to pore clogging. A global Sobol-Morris sensitivity analysis further reveals that the kinetic parameters of reactive minerals are the most influential factor, followed by wettability, while salinity has only a minor influence. Furthermore, these findings highlight that wettability is not merely a flow property but a fundamental control on CO 2 mineralization in basalts, with direct implications for site selection for storage projects.

Basalts↗
NASA NTRS2026

Development of a One-Domain Volume-Averaged Navier–Stokes Solver

The interaction between a high-enthalpy flow and a thermal protection material is inherently multiscale and multiphysics. In conventional aerothermal analyses, the external flow and material response are generally modeled using separate computational domains coupled through boundary conditions at the material surface. Although this approach has supported many practical applications, it requires assumptions about the location and behavior of the interface and may become difficult to apply when material decomposition, internal reactions, and surface recession substantially alter the porous structure. This report presents the development of a one-domain formulation in which the free-fluid and porous-material regions are represented within a single computational domain. The formulation is based on the volume-averaged Navier–Stokes (VANS) equations, derived from the governing equations for reacting, compressible flow and condensed material. Volume averaging transfers the influence of the unresolved material microstructure to the macroscale equations through effective transport properties, interfacial source terms, and dispersion fluxes. Particular attention is given to regions in which porosity and permeability vary rapidly, including the diffuse transition between a porous material and the surrounding fluid. The resulting equations are implemented in the Porous-material Analysis Toolbox based on OpenFOAM (PATO). The report describes the pressure–velocity coupling strategy used by the solver, examines spatial filtering techniques for deriving effective properties, and evaluates the influence of a smoothly varying interface permeability. Numerical demonstrations include canonical porous-flow configurations, a flow-tube configuration representative of FiberForm® permeability experiments, and the oxidation of a porous carbon material. The purpose of this work is to establish a mathematical and computational foundation for a unified treatment of flow and thermal protection material response. The present formulation is intended to support the progressive inclusion of additional physical processes, including multicomponent transport, finite-rate gas–surface chemistry, pyrolysis, internal oxidation, and material recession. It also provides a framework for connecting pore-scale simulations and microstructural characterization with macroscale aerothermal-response calculations. This report is intended for researchers and engineers working in computational fluid dynamics, porous-media transport, material response, and thermal protection system modeling. It documents both the theoretical development and the initial numerical assessment of the one-domain approach, while identifying the closure of effective and dispersion terms as an important subject for continued investigation.

Ablation↗
DOE OSTI2024

Accessing Fungal Contributions to the Birch Effect: Real-Time Respiration from Pore-Scale Microfluidics

Drying and rewetting of soil stimulates soil carbon emission. The Birch effect, driven by these cycles, leads to CO2 efflux, which can be monitored using real-time mass spectrometry (RTMS). Although soil fungi retain water during droughts, their contribution to CO2 release during drying–rewetting cycles remains unclear. In this study, we present the first demonstration of integrating micromodels with RTMS to monitor the Birch effect by simulating drought and rewetting. Micromodels were inoculated with axenic fungal culture and dried to assess moisture retention. After drying, RTMS quantified CO2 release upon rewetting with H218O mixtures. Our results showed that soil fungi released CO2 upon rehydration and immediately utilized the external water source at the pore scale by generating subsequent 46CO2. This work is the first to integrate RTMS with microsystems to investigate pore-scale biogeochemistry and the involvement of fungi in the Birch effect.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Quantitative local state of charge mapping by operando electrochemical fluorescence microscopy in porous electrodes

We introduce operando quantitative electrochemical fluorescence state of charge mapping (QEFSM), a non-invasive technique to study operating electrochemical systems along with a new design of optically transparent microfluidic redox flow cells compatible with the most demanding optical requirements. QEFSM allows quantitative mappings of the concentration of a particular oxidation state of a redox-active species within a porous electrode during its operation. In this study, we used confocal microscopy to map the fluorescence signal of the reduced form of 2,7-anthraquinone disulfonate (AQDS) in a set of multistep-chronoamperometry experiments. Calibrating these images and incorporating an analytical model of quinhydrone heterodimer formation with no free parameters, and accounting for the emission of each species involved, we determined the local molecular concentration and the state of charge (SOC) fields within a commercial porous electrode during operation. With this method, electrochemical conversion and species advection, reaction and diffusion can be monitored at heretofore unprecedented transverse and axial resolution (1 μm and 25 μm, respectively) at frame rates of 0.5 Hz, opening new routes to understanding local electrochemical processes in porous electrodes. Here, we observed pore-scale SOC inhomogeneities appearing when the fraction of electroactive species converted in a single pass through the electrode becomes large.

42 ENGINEERING↗
DOE OSTI2024

PYSIMFRAC: A Python library for synthetic fracture generation and analysis

In this paper, we introduce PYSIMFRAC, an open-source python library for generating 3-D synthetic fracture realizations, integrating with fluid simulators, and performing analysis. PYSIMFRAC allows the user to specify one of three fracture generation techniques (Box, Gaussian, or Spectral) and perform statistical analysis including the autocorrelation, moments, and probability density functions of the fracture surfaces and aperture. This analysis and accessibility of a python library allows the user to create realistic fracture realizations and vary properties of interest. In addition, PYSIMFRAC includes integration examples to two different pore-scale simulators and the discrete fracture network simulator, dfnWorks. The capabilities developed in this work provides opportunity for quick and smooth adoption and implementation by the wider scientific community for accurate characterization of fluid transport in geologic media. We present PYSIMFRAC along with integration examples and discuss the ability to extend PYSIMFRAC from a single complex fracture to complex fracture networks.

58 GEOSCIENCES↗
DOE OSTI2015

Pore-scale investigation on stress-dependent characteristics of granular packs and the impact of pore deformation on fluid distribution

Understanding the effect of changing stress conditions on multiphase flow in porous media is of fundamental importance for many subsurface activities including enhanced oil recovery, water drawdown from aquifers, soil confinement, and geologic carbon storage. Geomechanical properties of complex porous systems are dynamically linked to flow conditions, but their feedback relationship is often oversimplified due to the difficulty of representing pore-scale stress deformation and multiphase flow characteristics in high fidelity. In this work, we performed pore-scale experiments of single- and multiphase flow through bead packs at different confining pressure conditions to elucidate compaction-dependent characteristics of granular packs and their impact on fluid flow. A series of drainage and imbibition cycles were conducted on a water-wet, soda-lime glass bead pack under varying confining stress conditions. Simultaneously, X-ray micro-CT was used to visualize and quantify the degree of deformation and fluid distribution corresponding with each stress condition and injection cycle. Micro-CT images were segmented using a gradient-based method to identify fluids (e.g., oil and water), and solid phase redistribution throughout the different experimental stages. Changes in porosity, tortuosity, and specific surface area were quantified as a function of applied confining pressure. Results demonstrate varying degrees of sensitivity of these properties to confining pressure, which suggests that caution must be taken when considering scalability of these properties for practical modeling purposes. Changes in capillary number with confining pressure are attributed to the increase in pore velocity as a result of pore contraction. Furthermore, this increase in pore velocity was found to have a marginal impact on average phase trapping at different confining pressures.

58 GEOSCIENCES↗
DOE OSTI2023

Application of unsupervised deep learning to image segmentation and in-situ contact angle measurements in a CO 2 -water-rock system

Rock surface wettability is a critical property that regulates multiphase flows in porous media, which can be quantified using the surface contact angle (CA). X-ray micro-computed tomography (μCT) provides an effective approach to in-situ measurements of surface CAs. However, the CA measurement accuracy depends significantly on the quality of CT image segmentation, which is the clustering of CT pixels into separate phases. Inspired by this, we developed a deep learning (DL)-based CA measurement workflow. Motivated by the recent tremendous progress in unsupervised learning techniques and aiming to avoid expensive manual data annotations, an unsupervised DL pipeline for CT image segmentation was proposed and implemented, which includes unsupervised model training and post-processing. The unsupervised model training was driven by a novel loss function constrained with feature similarity and spatial continuity and implemented by iterative forward and backward paths; the former clustered the pixel-wise feature vectors extracted by convolution neural networks, whereas the latter updated the parameters using gradient descent. An over-segmentation strategy was adopted for model training. The post-processing steps based on agglomerative hierarchical clustering (AHC) were implemented to further merge the over-segmented model output to the desired cluster number, which is intended to improve the efficiency of image segmentation. The developed unsupervised DL pipeline was compared with other commonly-used image segmentation methods using pixel-wise and physics-based evaluation metrics on a synthetic raw-image dataset, which had a known ground truth. The unsupervised DL pipeline showed the best performance. Next, the segmented images were input to an automatic CA measurement tool, and the results were validated by comparisons with manual measurements. The CA values from the manual and automatic measurements showed similar distributions and statistical properties. The automatic measurement demonstrated a wider spectrum because of the much larger number of measurement data points. The primary novelty of the unsupervised DL pipeline developed in this study lies in the novel loss function and the over-segmentation strategy associated with AHC post-processing. Finally, the workflow has been proven an efficient tool for pore-scale wettability characterization, which has a wide range of applications in fundamental studies of multiphase flows in natural porous media, which have critical implications to geological carbon sequestration, hydrocarbon energy recovery, and contaminant transport in groundwater.

42 ENGINEERING↗
DOE OSTI2025

The impact of capillary heterogeneity on CO 2 flow and trapping across scales

Capillary heterogeneity has been identified over the last decade as a key control on subsurface CO 2 flow behavior during geological CO 2 sequestration. These heterogeneities can be formed in all sedimentary rocks, ranging from slight variations in the sand grain sizes to extensive sequences of interbedded sands, shales, and limestones. Capillary heterogeneity has been largely, although not entirely, overlooked in subsurface flow modeling because it is assumed to only directly influence fluid redistribution over scales of centimeters to meters. However, even small-scale fluid movements can result in dramatic impacts on the mobility and trapping of the CO 2 over kilometers. Therefore, neglecting capillary heterogeneity at multiple scales could potentially lead to errors in modeling and predicting field-scale plume migration. In this review paper, we aim to provide a consistent overview to (1) establish that capillary heterogeneity can have a major impact on CO 2 plume migration, (2) establish the respective length scales at which capillary heterogeneity matters, and (3) provide guidance for numerical modeling. This review covers pertinent literature and extracts key observations from the core to the field scales. Experimental studies have shown that millimeter-decimeter scale capillary heterogeneity can cause the so-called capillary heterogeneity trapping in addition to pore-scale residual trapping. Even at such a small scale, capillary heterogeneity can already lead to complex upscaled constitutive relationships, such as flow-rate dependent and anisotropic relative permeability, which affects field-scale CO 2 migration even when field-scale heterogeneities are present. Under gravity-dominated flow regimes, centimeter-meter scale capillary heterogeneity can entrap a significant amount of CO 2 at field scale, not just after imbibition but also during drainage. In certain cases, the presence of capillary heterogeneity can even completely stop the vertical movement of the CO 2 plume, hence greatly reducing leakage risks. At meter-kilometer scale, the influence of capillary heterogeneity is more pronounced and can hinder or redirect CO 2 migration in both lateral and vertical directions. The impact of capillary heterogeneity across multiple spatial scales poses a great challenge in modeling CO 2 migration at field scale, because it is practically impossible to build a field-scale earth model with grid blocks at millimeter scale. We recommend a hierarchical modeling approach to address this challenge. At field scale, earth models are built to capture geological features and heterogeneities in high but still practical grid resolutions. For each facies or rock type of the field-scale model, high- resolution meter-scale “conceptual” models are built with millimeter-scale grid blocks to capture representative fine-scale bedding geometries and heterogeneities in various environments of deposition, bridging the gap from subcore scale to the size of a field-scale simulation grid block. Upscaling is then used to preserve the smaller-scale flow dynamics of various rock types in field-scale simulations. Here, future work is needed to (1) refine, improve, and validate the hierarchical modeling approach; (2) build libraries of fine-scale bedding models for facies in various environments of deposition; (3) quantify multiscale capillary heterogeneity effects under subsurface uncertainties; (4) gain learning from different storage formations; and (5) establish best practices that balance accuracy and computational speed.

Capillary heterogeneity↗
DOE OSTI2023

Effective permeability of an immiscible fluid in porous media determined from its geometric state

Based on the phenomenological extension of Darcy's law, two-fluid flow is dependent on a relative permeability function of saturation only that is process or path dependent with an underlying dependency on pore structure and wettability. For applications (fuel cells to underground CO 2 storage), it is imperative to determine the effective phase permeability relationships where the traditional approach is based on the inverse modeling of time-consuming experiments. The underlying reason is that the fundamental upscaling step from pore to Darcy scale, which links the pore structure of the porous medium to the continuum hydraulic conductivities, is not solved. Herein, we develop an artificial neural network (ANN) that relies on fundamental geometrical relationships to determine the mechanical energy dissipation during creeping immiscible two-fluid flow. Finally, the developed ANN is based on a prescribed set of state variables based on physical insights that predict the effective permeability of 4500 unseen pore-scale geometrical states with R 2 = 0.98.

42 ENGINEERING↗
DOE OSTI2023

A Comparative Study of Deep Learning Models for Fracture and Pore Space Segmentation in Synthetic Fractured Digital Rocks

This study focuses on the comparative study of deep learning (DL) models for pore space and discrete fracture networks (DFNs) segmentation in synthetic fractured digital rocks, specifically targeting low-permeability rock formations, such as shale and tight sandstones. Accurate characterization of pore space and DFNs is critical for subsequent property analysis and fluid flow modeling. Four DL models, SegNet, U-Net, U-Net-wide, and nested U-Net (i.e., U-Net++), were trained, validated, and tested using synthetic datasets, including input and label image pairs with varying properties. The model performance was assessed regarding pixel-wise metrics, including the F1 score and pixel-wise difference maps. In addition, the physics-based metrics were considered for further analysis, including sample porosity and absolute permeability. Particularly, We first simulated the permeability of porous media containing only pore space and then simulated the permeability of porous media with DFNs added. The difference between these two values is used to quantify the connectivity of segmented DFNs, which is an important parameter for low-permeability rocks. The pixel-wise metrics showed that the nested U-Net model outperformed the rest of the DL models in pore space and DFNs segmentation, with the SegNet model exhibiting the second-best performance. Particularly, nested U-Net enhanced segmentation accuracy for challenging boundary pixels affected by partial volume effects. The U-Net-wide model achieved improved accuracy compared to the U-Net model, which indicated the influence of parameter numbers. Similarly, nested U-Net has the closest match to the ground truth of physics-based metrics, including the porosity of pore space and DFNs, and the permeability difference quantifying the connectivity of DFNs. The findings highlight the effectiveness of DL models, especially the U-Net++ model with nested architecture and redesigned skip connections, in accurately segmenting pore spaces and DFNs, which are crucial for pore-scale fluid flow and transport simulation in low-permeability rocks.

Wang, Hongsheng↗