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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Review: Pre-Darcy flows in low-permeability porous media

The widely used Darcy’s law specifies a linear relation between the Darcy velocity of fluid flow and the pressure gradient that drives the flow. However, studies have shown that Darcy velocity can exhibit a nonlinear dependence on the pressure gradient in low-permeability porous media such as clay and shale when the pressure gradient is adequately low. This phenomenon is referred to as low-velocity non-Darcian flow or pre-Darcy flow. This paper provides a comprehensive review of the theories, experimental data, and modeling methods for pre-Darcy flow in low-permeability porous media. The review begins by outlining the fundamental mechanisms underlying pre-Darcy flow that regulate the unique characteristics such as nonlinear dependence of the Darcy velocity on the pressure gradient and its relevance to fluid–rock interactions. The review then proceeds to present a thorough compilation of experimental investigations performed in various low-permeability geomaterials including tight sandstones, shales, and clays. Next, empirical and theoretical models and simulation methods that have been developed to fit and interpret experimental data are reviewed. Finally, the review underscores the challenges encountered in conducting and interpreting pre-Darcy flow experiments and suggests future research directions. By analyzing previous experimental investigations, this review aims to offer a valuable resource for researchers and practitioners seeking to enhance their understanding of fluid dynamics in low-permeability geomaterials. This provides insights into the application of pre-Darcy flow in numerous natural and engineered processes such as shale oil and gas recovery, contaminant transport in low-permeability aquifers, and geological disposal of nuclear waste.

58 GEOSCIENCES↗
DOE OSTI2024

Learning a general model of single phase flow in complex 3D porous media

Modeling effective transport properties of 3D porous media, such as permeability, at multiple scales is challenging as a result of the combined complexity of the pore structures and fluid physics—in particular, confinement effects which vary across the nanoscale to the microscale. While numerical simulation is possible, the computational cost is prohibitive for realistic domains, which are large and complex. Although machine learning (ML) models have been proposed to circumvent simulation, none so far has simultaneously accounted for heterogeneous 3D structures, fluid confinement effects, and multiple simulation resolutions. By utilizing numerous computer science techniques to improve the scalability of training, we have for the first time developed a general flow model that accounts for the pore-structure and corresponding physical phenomena at scales from Angstrom to the micrometer. Using synthetic computational domains for training, our ML model exhibits strong performance (R 2 = 0.9) when tested on extremely diverse real domains at multiple scales.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Learning a General Model of Single Phase Flow in Complex 3D Porous Media

Modeling effective transport properties of 3D porous media, such as permeability, at multiple scales is challenging as a result of the combined complexity of the pore structures and fluid physics—in particular, confinement effects which vary across the nanoscale to the microscale. While numerical simulation is possible, the computational cost is prohibitive for realistic domains, which are large and complex. Although machine learning (ML) models have been proposed to circumvent simulation, none so far has simultaneously accounted for heterogeneous 3D structures, fluid confinement effects, and multiple simulation resolutions. By utilizing numerous computer science techniques to improve the scalability of training, we have for the first time developed a general flow model that accounts for the pore-structure and corresponding physical phenomena at scales from Angstrom to the micrometer. Using synthetic computational domains for training, our ML model exhibits strong performance (R 2 = 0.9) when tested on extremely diverse real domains at multiple scales.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A Comparative Study of Compressive Effects on the Morphology and Performance of Carbon Paper and Cloth Electrodes in Redox Flow Batteries

Compressing porous carbon electrodes is a common approach to improve flow battery performance, but the resulting impact on electrode structure, fluid dynamics, and cell performance is not well understood. Herein, microtomographic imaging, load cell testing, and flow cell diagnostics are employed to characterize how compression‐induced changes impact pressure drop, polarization, and mass‐transfer scaling. Five different compressions are tested, spanning ranges typically used in literature, for AvCarb 1071 cloth (0%, 9%, 20%, 25%, 32%) and Freudenberg H23 paper (0%, 8%, 12%, 17%, 22%). It is found that the two electrode structures have distinct responses to compression, resulting in differing optimal conditions identified for each material; specifically, the Freudenberg H23 exhibits lower combined ohmic, charge‐transfer, and mass‐transport values at 8% compression, resulting in improved electrochemical performance across all compressive values, as compared to the optimal AvCarb 1071 compression (20%). Overall, Freudenberg H23 exhibits a greater sensitivity to compression with peak electrochemical activity correlating with increased permeability, whereas AvCarb 1071 is insensitive to compressive loads but produces lower electrochemical performance. Herein, the trade‐offs of mechanical robustness on fluid‐dynamic and electrochemical performance between the two electrodes are demonstrated by the aforementioned findings, suggesting each could be used for specific operating environments.

25 ENERGY STORAGE↗
DOE OSTI2026

AnisONet: A deep neural operator-based anisotropic permeability upscaler from pore to Darcy scale

Directional permeability variations, which govern directional fluid flow in porous media with anisotropy, are important to accurately predict flow behavior, reactive transport, and fluid–solid interactions for various processes such as enhanced geothermal systems, energy storage devices, and biological systems. However, the intricate architecture of porous media makes it difficult to predict directional permeabilities. In this work, we present a novel machine learning (ML) framework, AnisONet, built upon an integration of a convolutional neural network, Swin transformer, and the deep operator network architecture, designed to predict anisotropic permeability and upscale predictions to larger spatial domains. First, AnisONet was evaluated with three classes of two-dimensional (2D) porous media, including synthetic circular and elliptical grains and natural sandstone grains from micro-computed tomography images. A lattice Boltzmann model (LBM) was used to calculate directional permeabilities at every 10° angle, producing 19 data points per image of porous media. AnisONet is then trained to predict permeability as a function of rotation angle. AnisONet showed strong predictive capability of directional permeability. Second, we tested our model for five upscaling cases with a large image size in the finite-element method (FEM) for 2D Darcy flow with various permeability tensor construction methods. Overall, upscaled permeability tensors in FEM simulations produce a reasonably good match with LBM results, highlighting the importance of selecting appropriate tensor formation strategies for accurate permeability upscaling. AnisONet, as a directional permeability estimator, could be further developed for more complex geometries, with the potential to develop a foundational ML model for various applications in porous media.

42 ENGINEERING↗
NASA NTRS2026

Advances in Entry Systems Modeling: Modeling Summer Visit 2025 Technical Reports

This NASA Technical Memorandum presents the collective work carried out during the Modeling Summer Visit (MSV) 2025, a collaborative research program between NASA Ames Research Center and three leading European research institutions: the University of Bordeaux, the von Karman Institute (VKI), and Ecole Polytechnique. Held from July 7th to August 1st, 2025, the NASA ARC MSV program brought together 42 researchers from Europe to work alongside NASA staff on 22 projects in entry systems modeling. The program was organized by Bruno Dias, Sergio Fraile-Izquierdo, and Jeremie Meurisse from Analytical Mechanics Associates, Inc., in collaboration with Marc Massot (Ecole Polytechnique), Jean Lachaud (University of Bordeaux), and Thierry Magin (VKI). The MSV program traces its origins to an initiative started by Nagi N. Mansour in 2018, with this 2025 edition representing a consolidation and expansion of that original vision. The projects were organized into six thematic groups: Porous Media, Numerical Methods, Plasma/Rarefied Methods, Experimental Reconstruction, Flow and Material Coupling Methods, and Transition and High-Speed Flows. Throughout the four-week program, participants presented their work in three public presentations (July 7th, July 21st, and August 1st), allowing for continuous feedback and discussion of their evolving research.

Plasmas↗
DOE OSTI2021

Non-Solvent Induced Phase Separation Enables Designer Redox Flow Battery Electrodes

Porous carbonaceous electrodes are performance-defining components in redox flow batteries (RFBs), where their properties impact the efficiency, cost, and durability of the system. The overarching challenge is to simultaneously fulfill multiple seemingly contradictory requirements—i.e., high surface area, low pressure drop, and facile mass transport—without sacrificing scalability or manufacturability. Here, non-solvent induced phase separation (NIPS) is proposed as a versatile method to synthesize tunable porous structures suitable for use as RFB electrodes. The variation of the relative concentration of scaffold-forming polyacrylonitrile to pore-forming poly(vinylpyrrolidone) is demonstrated to result in electrodes with distinct microstructure and porosity. Tomographic microscopy, porosimetry, and spectroscopy are used to characterize the 3D structure and surface chemistry. Flow cell studies with two common redox species (i.e., all-vanadium and Fe2+/3+) reveal that the novel electrodes can outperform traditional carbon fiber electrodes. It is posited that the bimodal porous structure, with interconnected large (>50 µm) macrovoids in the through-plane direction and smaller (<5 µm) pores throughout, provides a favorable balance between offsetting traits. Although nascent, the NIPS synthesis approach has the potential to serve as a technology platform for the development of porous electrodes specifically designed to enable electrochemical flow technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Improving deep learning performance for predicting large-scale geological ${{CO}_{2}}$ sequestration modeling through feature coarsening

Physics-based reservoir simulation for fluid flow in porous media is a numerical simulation method to predict the temporal-spatial patterns of state variables (e.g. pressure p) in porous media, and usually requires prohibitively high computational expense due to its non-linearity and the large number of degrees of freedom (DoF). This work describes a deep learning (DL) workflow to predict the pressure evolution as fluid flows in large-scale 3-dimensional(3D) heterogeneous porous media. In particular, we develop an efficient feature coarsening technique to extract the most representative information and perform the training and prediction of DL at the coarse scale, and further recover the resolution at the fine scale by spatial interpolation. We validate the DL approach to predict pressure field against physics-based simulation data for a field-scale 3D geologic CO 2 sequestration reservoir model. We evaluate the impact of feature coarsening on DL performance, and observe that the feature coarsening not only decreases the training time by >74% and reduces the memory consumption by >75%, but also maintains temporal error 0.63% on average. Besides, the DL workflow provides predictive efficiency with 1406 times speedup compared to physics-based numerical simulation. The key findings from this research significantly improve the training and prediction efficiency of deep learning model to deal with large-scale heterogeneous reservoir models, and thus it can also be further applied to accelerate workflows of history matching and reservoir optimization for close-loop reservoir management.

58 GEOSCIENCES↗
NASA NTRS1969

Two phase flow and heat transfer in porous beds under variable body forces, part 2

Analytical and experimental investigations of a pilot model of a channel for the study of two-phase flow under low or zero gravity are presented. The formulation of dimensionless parameters to indicate the relative magnitude of the effects of capillarity, gravity, pressure gradient, viscosity, and inertia is described. The investigation is based on the principal equations of fluid mechanics and thermodynamics. Techniques were investigated by using a laser velocimeter for measuring point velocities of the fluid within the porous material without disturbing the flow.

Evers, J. L.↗
NASA NTRS1980

Flow over plates with suction through porous strips

This paper addresses the steady, incompressible, two-dimensional flow past a flat plate with suction through porous strips. Closed-form solutions for each flow quantity are developed in the context of linearized triple-deck theory using Fourier transforms. To demonstrate the validity of these closed-form solutions, we compare the wall shear stress and pressure coefficients and the streamwise velocity profiles from the linearized theory with those obtained by the numerical integration of both interacting and nonsimilar boundary-layer equations. The agreement between the linearized triple-deck and interacting boundary-layer equations is good; however, the nonsimilar boundary layers, which fail to account for upstream influence, are shown to be in poor agreement with both interacting boundary layers and the linearized triple deck. The linearized closed-form solutions will therefore be very useful in future stability calculations.

Nayfeh, A. H.↗
DOE OSTI2021

Pore-Scale Dynamics of Liquid CO2–Water Displacement in 2D Axisymmetric Porous Micromodels Under Strong Drainage and Weak Imbibition Conditions: High-Speed μPIV Measurements

Resolving pore-scale transient flow dynamics is crucial to understanding the physics underlying multiphase flow in porous media and informing large-scale predictive models. Surface properties of the porous matrix play an important role in controlling such physics, yet interfacial mechanisms remain poorly understood, in part due to a lack of direct observations. This study reports on an experimental investigation of the pore-scale flow dynamics of liquid CO 2 and water in two-dimensional (2D) circular porous micromodels with different surface characteristics employing high-speed microscopic particle image velocimetry (μPIV). The design of the micromodel minimized side boundary effects due to the limited size of the domain. The high-speed μPIV technique resolved the spatial and temporal dynamics of multiphase flow of CO 2 and water under reservoir-relevant conditions, for both drainage and imbibition scenarios. When CO 2 displaced water in a hydrophilic micromodel (i.e., drainage), unstable capillary fingering occurred and the pore flow was dominated by successive pore-scale burst events (i.e., Haines jumps). When the same experiment was repeated in a nearly neutral wetting micromodel (i.e., weak imbibition), flow instability and fluctuations were virtually eliminated, leading to a more compact displacement pattern. Energy balance analysis indicates that the conversion efficiency between surface energy and external work is less than 30%, and that kinetic energy is a disproportionately smaller contributor to the energy budget. This is true even during a Haines jump event, which induces velocities typically two orders of magnitude higher than the bulk velocity. These novel measurements further enabled direct observations of the meniscus displacement, revealing a significant alteration of the pore filling mechanisms during drainage and imbibition. While the former typically featured burst events, which often occur only at one of the several throats connecting a pore, the latter is typically dominated by a cooperative filling mechanism involving simultaneous invasion of a pore from multiple throats. This cooperative filling mechanism leads to merging of two interfaces and releases surface energy, causing instantaneous high-speed events that are similar, yet fundamentally different from, burst events. Finally, pore-scale velocity fields were statistically analyzed to provide a quantitative measure of the role of capillary effects in these pore flows.

Li, Yaofa↗
NASA NTRS1990

Experimental Investigation of Porous-floor Effects on Cavity Flow Fields at Supersonic Speeds

An experimental investigation was conducted to determine the effectiveness of a passive-venting system to modify the flow field characteristics of a rectangular-box cavity at supersonic speeds. The passive-venting system consists of a porous floor with a vent chamber beneath the floor. For certain cavity length-to-height ratios, this configuration allowed high-pressure air at the rear of the cavity to vent to the forward part of the cavity, thereby modifying the cavity flow field. The wind-tunnel model consisted of a flat plate that housed a cavity mounted on a balance such that only the cavity drag was measured. The cavity height remained constant, and the length varied with rectangular-block inserts. Both solid-and porous-floor cavities were tested for comparison at Mach numbers of 1.60, 1.90, 2.16, and 2.86. These results showed that the passive-venting system did modify the cavity flow field. In order to determine the type flow field which existed for the porous-floor configuration, pressures were measured inside the cavity at the same conditions and for the same configurations as those used in the drag tests. Pressure data were also obtained with stores mounted in the cavity. These results, along with Schlieren photographs and the tabulated data, are presented to document the porous-floor cavity flow field.

Wilcox, Floyd J., Jr.↗
DOE OSTI2025

Unsteady- and Steady-State Relative Permeability Study with X-ray and Acoustic Monitoring for CO 2 Storage in Deep Saline Aquifers

In this study, we link the multiphase flow measurements with controls of sedimentary structures (e.g., heterogeneity and anisotropy) on relative permeability to variations in ultrasonic velocities for two deep saline aquifer formations (Entrada and Bluff Sandstones) in the San Juan Basin of the Southwestern USA. The rock specimens were extracted from outcrop sites near Durango, CO, USA. They have distinct differences in grain size, cementation composition, and individual chemical amounts, despite both formations being eolian sandstones. We performed a series of unsteady- and steady-state CO 2 -brine relative permeability experiments under capillary-controlled displacement rates. Unsteady-state experiments were conducted at 71 °C and 9.65 MPa; steady-state experiments were conducted at 85 °C and 22.8 MPa and 89 °C and 24.1 MPa for the Bluff and Entrada Sandstones, respectively. During the unsteady experiments, X-ray computed tomography was used to visualize multiphase flow in porous media and quantify saturations during brine drainage under various flow rates. Scan images and saturation profiles indicate that the CO 2 distribution in the pore volume was strongly impacted by the presence of high-angle cross-laminations, heterogeneous rock structure, and direction of bedding orientation. Those factors contribute to dramatic and quick initial breakthroughs and affect the overall saturation dynamics. Steady-state relative permeability tests were conducted at net flow rates of 1 mL/min for both brine drainage and imbibition. During the experimental steps, the CO 2 fractional flow was increased and decreased for both drainage and imbibition scenarios to mimic the front when CO 2 contacts brine and behind the front when brine enters space previously occupied by CO 2 . It was found that compressional velocity decreased, while shear waves slightly increased as brine saturation decreased. The hysteresis effects for the relative permeability and acoustic velocities were distinct. Furthermore, the CO 2 /brine front stability is quantified by applying a mobility ratio approach to spot saturations at which the boundary line between fluids becomes uneven. The results presented in this work can potentially boost the quality and precision of forecasts for the CO 2 storage projects in which the vertical and horizontal core-scale heterogeneity and anisotropy impact the plume migration within host reservoirs.

carbon dioxide (CO2)↗
DOE OSTI2022

Gene flow and introgression are pervasive forces shaping the evolution of bacterial species

Abstract Background Although originally thought to evolve clonally, studies have revealed that most bacteria exchange DNA. However, it remains unclear to what extent gene flow shapes the evolution of bacterial genomes and maintains the cohesion of species. Results Here, we analyze the patterns of gene flow within and between >2600 bacterial species. Our results show that fewer than 10% of bacterial species are truly clonal, indicating that purely asexual species are rare in nature. We further demonstrate that the taxonomic criterion of ~95% genome sequence identity routinely used to define bacterial species does not accurately represent a level of divergence that imposes an effective barrier to gene flow across bacterial species. Interruption of gene flow can occur at various sequence identities across lineages, generally from 90 to 98% genome identity. This likely explains why a ~95% genome sequence identity threshold has empirically been judged as a good approximation to define bacterial species. Our results support a universal mechanism where the availability of identical genomic DNA segments required to initiate homologous recombination is the primary determinant of gene flow and species boundaries in bacteria. We show that these barriers of gene flow remain porous since many distinct species maintain some level of gene flow, similar to introgression in sexual organisms. Conclusions Overall, bacterial evolution and speciation are likely shaped by similar forces driving the evolution of sexual organisms. Our findings support a model where the interruption of gene flow—although not necessarily the initial cause of speciation—leads to the establishment of permanent and irreversible species borders.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1951

Coolant-Flow Calibrations of Three Simulated Porous Gas-Turbine Blades

An investigation was conducted at the NACA Lewis laboratory to determine whether simulated porous gas-turbine blades fabricated by the Eaton Manufacturing Company of Cleveland, Ohio would be satisfactory with respect to coolant flow for application in gas-turbine engines. These blades simulated porous turbine blades by forcing the cooling air onto the blade surface through a large number of chordwise openings or slits between laminations of sheet metal or wire. This type of surface has a finite number of openings, whereas a porous surface has an almost infinite number of smaller openings for the coolant flow. The investigation showed that a blade made of sheet-metal laminations stacked on a support member that passed up through the coolant passage was completely unsatisfactory because of extremely poor coolant flow distribution over the blade surface. The flow distribution for two wire-wound blades was more uniform, but the pressure drop between the coolant supply pressure and the local pressure on the outside of the blades was too low by a factor ranging from 3 to 3.5 for the required coolant flow rates. The pressure drop could be increased by forcing the wires closer together during blade fabrication.

Esger, Jack B.↗