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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↗

DOE OSTI2024

Inertia-induced mixing and reaction maximization in laminar porous media flows

Solute transport and biogeochemical reactions in porous and fractured media flows are controlled by mixing, as are subsurface engineering operations such as contaminant remediation, geothermal energy production, and carbon sequestration. Porous media flows are generally regarded as slow, so the effects of fluid inertia on mixing and reaction are typically ignored. Here, we demonstrate through microfluidic experiments and numerical simulations of mixing-induced reaction that inertial recirculating flows readily emerge in laminar porous media flows and dramatically alter mixing and reaction dynamics. An optimal Reynolds number that maximizes the reaction rate is observed for individual pore throats of different sizes. This reaction maximization is attributed to the effects of recirculation flows on reactant availability, mixing, and reaction completion, which depend on the topology of recirculation relative to the boundary of the reactants or mixing interface. Recirculation enhances mixing and reactant availability, but a further increase in flow velocity reduces the residence time in recirculation, leading to a decrease in reaction rate. The reaction maximization is also confirmed in a flow channel with grain inclusions and randomized porous media. Interestingly, the domain-wide reaction rate shows a dramatic increase with increasing Re in the randomized porous media case. This is because fluid inertia induces complex three-dimensional flows in randomized porous media, which significantly increases transverse spreading and mixing. This study shows how inertial flows control reaction dynamics at the pore scale and beyond, thus having major implications for a wide range of environmental systems.

Chen, Michael A. (ORCID:0000000294614710)↗

DOE OSTI2025

Alquimia v1.0: a generic interface to biogeochemical codes – a tool for interoperable development, prototyping and benchmarking for multiphysics simulators

Alquimia v1.0 is a generic interface to geochemical solvers that facilitates development of multiphysics simulators by enabling code coupling, prototyping and benchmarking. The interface enforces the function arguments and their types for setting up, solving, serving up output data and carrying out other common auxiliary tasks while providing a set of structures for data transfer between the multiphysics code driving the simulation and the geochemical solver. Alquimia relies on a single-cell approach that permits operator splitting coupling and parallel computation. We describe the implementation in Alquimia of two widely used open-source codes that perform geochemical calculations: PFLOTRAN and CrunchFlow. We then exemplify its use for the implementation and simulation of reactive transport in porous media by two open-source flow and transport simulators: Amanzi and ParFlow. We also demonstrate its use for the simulation of coupled processes in novel multiphysics applications including the effect of multiphase flow on reaction rates at the pore scale with OpenFOAM, the role of complex biogeochemical processes in land surface models such as the E3SM Land Model (ELM) and the impact of surface–subsurface hydrological interactions on hydrogeochemical export from watersheds with the Advanced Terrestrial Simulator (ATS). These applications make it apparent that the availability of a well-defined yet flexible interface has the potential to improve the software development workflow, freeing up resources to focus on advances in process models and mechanistic understanding of coupled problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Characterization and Sampling of Ultralow Permeability Geomaterials using Electrokinetics (LDRD Final Report 209234)

This final report on Laboratory Directed Research and Development (LDRD) project 209234 presents background material for electrokinetics at the pore and porous media scales. We present some theoretical developments related to uncoupling electrokinetic flow solutions, from a manuscript recently accepted into Mathematical Geosciences for publication. We present a summary of two pore-scale modeling efforts undertaken as part of the academic alliance with University of Illinois, resulting in one already submitted journal publication to Transport in Porous Media and another in preparation for submission to a journal. We finally show the laboratory apparatus built in Laboratory B59 in Building 823 and discuss some of the issues that occurred with it.

58 GEOSCIENCES↗

DOE OSTI2020

Transport Simulations on Scanning Transmission Electron Microscope Images of Nanoporous Shale

Digital rock physics is an often-mentioned approach to better understand and model transport processes occurring in tight nanoporous media including the organic and inorganic matrix of shale. Workflows integrating nanometer-scale image data and pore-scale simulations are relatively undeveloped, however. In this paper, a workflow is demonstrated progressing from sample acquisition and preparation, to image acquisition by Scanning Transmission Electron Microscopy (STEM) tomography, to volumetric reconstruction to pore-space discretization to numerical simulation of pore-scale transport. Key aspects of the workflow include (i) STEM tomography in high angle annular dark field (HAADF) mode to image three-dimensional pore networks in µm-sized samples with nanometer resolution and (ii) lattice Boltzmann method (LBM) simulations to describe gas flow in slip, transitional, and Knudsen diffusion regimes. It is shown that STEM tomography with nanoscale resolution yields excellent representation of the size and connectivity of organic nanopore networks. In turn, pore-scale simulation on such networks contributes to understanding of transport and storage properties of nanoporous shale. Interestingly, flow occurs primarily along pore networks with pore dimensions on the order of tens of nanometers. Smaller pores do not form percolating pathways in the sample volume imaged. Apparent gas permeability in the range of 10−19 to 10−16 m2 is computed.

42 ENGINEERING↗

DOE OSTI2024

Enforcing global constraints for the dispersion closure problem: τ 2 -SIMPLE algorithm

Permeability and effective dispersion tensors are critical parameters to characterize flow and transport in porous media at the continuum scale. Homogenization theory defines a framework in which such effective properties are first computed from solving a closure problem in a repeating unit cell of the periodic microstructure and then used in a macroscopic formulation for efficient computation. The closure problem is formulated as a local boundary value problem subjected to global constraints, which guarantee the uniqueness of the solution and can be difficult to satisfy for complex geometries and at high flow conditions. These constraints also ensure that pore-scale pressure, velocity, and concentration fields can be accurately reconstructed from the closure variable. Building on a previous work, here we present a framework that allows to satisfy global constraints associated to both the permeability and the dispersion closure problems by introducing two artificial time scales. The algorithm, called τ 2 -SIMPLE, computes both permeability and effective dispersion given an arbitrarily complex geometry and flow condition. Furthermore, this algorithm is demonstrated to be accurate for both 2D and 3D geometries across varying flow conditions, and thus it can be used to quickly characterize effective properties from porous media images in many applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Pore-Scale Analysis of the Permeability Damage and Recovery during Cyclic Freshwater and Brine Injection in Porous Media Containing Non-Swelling Clays

Permeability damage in subsurface porous media caused by clay mobilization is encountered in many engineering applications, such as geothermal energy, water disposal, oil recovery, and underground CO2 storage. During the freshwater injection into rocks containing brine, the sudden decrease in salinity causes native clay fines to detach and clog pore throats, leading to a significant decline in permeability. The clay fines detach due to weakened net-attractive forces binding them to each other and the grain. Past experiments link this permeability damage on the immediate history of the salinity and the direction of flow. To better understand this phenomenon, we conducted pore-scale simulations of cyclic injection of freshwater and brine into sandstone containing Kaolinite clay. Our simulations establish a link between the clay-fine trajectory and the permeability trend observed by Khilar and Fogler (1983). For a uniform clay size of 3 microns, we observe a permeability decline by two orders of magnitude during freshwater injection with respect to brine injection. Increasing salinity and simultaneously reversing flow direction restores the permeability. The permeability restoration upon reversing the brine flow direction is attributed to the unblocking of pore throats in the reverse direction by the movement of the clay particles along the grain surfaces by the hydrodynamic force and the strong net-attractive force under high salinity.

Bhuvankar, Pramod (ORCID:000000027739973X)↗

DOE OSTI2021

Multiscale Assessment of Caprock Integrity for Geologic Carbon Storage in the Pennsylvanian Farnsworth Unit, Texas, USA

Leakage pathways through caprock lithologies for underground storage of CO2 and/or enhanced oil recovery (EOR) include intrusion into nano-pore mudstones, flow within fractures and faults, and larger-scale sedimentary heterogeneity (e.g., stacked channel deposits). To assess multiscale sealing integrity of the caprock system that overlies the Morrow B sandstone reservoir, Farnsworth Unit (FWU), Texas, USA, we combine pore-to-core observations, laboratory testing, well logging results, and noble gas analysis. A cluster analysis combining gamma ray, compressional slowness, and other logs was combined with caliper responses and triaxial rock mechanics testing to define eleven lithologic classes across the upper Morrow shale and Thirteen Finger limestone caprock units, with estimations of dynamic elastic moduli and fracture breakdown pressures (minimum horizontal stress gradients) for each class. Mercury porosimetry determinations of CO2 column heights in sealing formations yield values exceeding reservoir height. Noble gas profiles provide a “geologic time-integrated” assessment of fluid flow across the reservoir-caprock system, with Morrow B reservoir measurements consistent with decades-long EOR water-flooding, and upper Morrow shale and lower Thirteen Finger limestone values being consistent with long-term geohydrologic isolation. Together, these data suggest an excellent sealing capacity for the FWU and provide limits for injection pressure increases accompanying carbon storage activities.

58 GEOSCIENCES↗

DOE OSTI2022

A Dynamic Pore Network Model for Imbibition Simulation Considering Corner Film Flow

Wetting films can develop in the corners of angular pores under strong wetting conditions. Modeling the dynamics of corner film remains elusive using direct numerical simulations because of the significant scale difference between main meniscus and corner film flow. In this paper, the modified interacting capillary bundle model (ICB), developed in our previous work to describe accurately corner film dynamics in a single square tube, is incorporated into a single-pressure dynamic pore network model (DPNM) to simulate imbibition in strongly wetting porous media with corner film flow. The traditional pore network is decomposed into several layers of interacting subpore networks where the 0th layer of subpore network simulates the main meniscus flow and higher layers the corner film flow. The fluid flow between different layers is captured by interlayer throats. In addition, the snap-off mechanism caused by the thickening of wetting corner film is considered. The accuracy of the developed model is validated for four cases: spontaneous imbibition in a single square tube, wetting fluid redistribution through corner films under a capillary pressure difference, snap off in a narrow throat connecting two large pores, and imbibition dynamics in a real microfluidic porous geometry. The validated model is then used to simulate both spontaneous and controlled imbibition in a pore network with random pore size distribution. Finally, the interaction between corner film and main meniscus flow in porous media is analyzed from a pore-scale perspective.

58 GEOSCIENCES↗

DOE OSTI2025

A Percolating Path to Green Iron

About 1.9 gigatonnes of steel is produced every year emitting 7% (2.7 gigatonnes) of global CO 2 in the process. More than 50% of the CO 2 emissions come from a single step of steelmaking, known as ironmaking. Hydrogen based direct reduction (HyDR) of iron oxide to iron has emerged as an emissions free ironmaking alternative. However multi-scale phenomena ranging from nanometers to meters inside HyDR reactors exhibit detrimental microstructure evolution which resists gaseous transport of H 2 /H 2 O, slows reaction rates and disrupts continuous reactor operation. To resolve the conundrum between atomic and reactor scales, we devise a percolation-theory model to reconcile nanoscale porosity with macroscopic properties relevant to reactor design models. Using synchrotron nano X-ray computed-tomography, we quantify the evolution of pores in iron oxide pellets, and demonstrate how nano-scale pore networks influence micro and macro-scale flow properties such as permeability, diffusivity and tortuosity. Our new modeling framework bridges the gap between scales and offers the criteria to accelerate HyDR by at least 5x via feedstock-reactor synergies based on percolation.

Paul, Subhechchha↗

DOE OSTI2022

Cavitation in a soft porous material

Abstract We study the collapse and expansion of a cavitation bubble in a deformable porous medium. We develop a continuum-scale model that couples compressible fluid flow in the pore network with the elastic response of a solid skeleton. Under the assumption of spherical symmetry, our model can be reduced to an ordinary differential equation that extends the Rayleigh–Plesset equation to bubbles in soft porous media. The extended Rayleigh–Plesset equation reveals that finite-size effects lead to the breakdown of the universal scaling relation between bubble radius and time that holds in the infinite-size limit. Our data indicate that the deformability of the porous medium slows down the collapse and expansion processes, a result with important consequences for wide-ranging phenomena, from drug delivery to spore dispersion.

Leng, Yu↗

DOE OSTI2021

Contributions of biofilm-induced flow heterogeneities to solute retention and anomalous transport features in porous media

We report that microbial biofilms are ubiquitous within porous media and the dynamics of their growth influence surface and subsurface flow patterns which impacts the physical properties of porous media and large-scale transport of solutes. Here, a two-dimensional pore-scale numerical model was used to evaluate the impact of biofilm-induced flow heterogeneities on conservative transport. Our study integrates experimental biofilm images of Paenibacillus 300A strain in a microfluidic device packed with cylindrical grains in a hexagonal distribution, with mathematical modeling. Biofilm is represented as a synthetic porous structure with locally varying physical properties that honors the impact of biofilm on the porous medium. We find that biofilm plays a major role in shaping the observed conservative transport dynamics by enhancing anomalous characteristics. More specifically, when biofilm is present, the pore structure in our geometry becomes more spatially correlated. We observe intermittent behavior in the Lagrangian velocities that switches between fast transport periods and long trapping events. Our results suggest that intermittency enhances solute spreading in breakthrough curves which exhibit extreme anomalous slope at intermediate times and very marked late solute arrival due to solute retention. The efficiency of solute retention by the biofilm is controlled by a transport regime which can extend the tailing in the concentration breakthrough curves. These results indicate that solute retention by the biofilm exerts a strong control on conservative solute transport at pore-scale, a role that to date has not received enough attention.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Numerical modeling of ion transport and adsorption in porous media: A pore-scale study for capacitive deionization desalination

In this report a pore-scale model is presented to simulate the dynamic ion transport and adsorption processes in porous electrodes used for capacitive deionization (CDI). The Stokes equation governing water flow is solved using the lattice Boltzmann method and Nernst-Planck equation describing ion transport is solved using the finite volume method. The ion adsorption process is considered at the surface of carbon electrodes. After validation against analytical solutions and published results, the model is used to study the coupled water flow, ion transport and adsorption in both two-dimensional and three-dimensional porous CDI electrodes at the pore scale. The effect of electrode microstructure, electrical potential and flow velocity on the adsorption processes is quantitatively investigated, and the relative importance of various parameters is determined. The presented model can be a powerful numerical tool to quantitatively analyze ion transport and adsorption in porous electrodes, and may provide useful information for the design and optimization of CDI electrodes and operating conditions for desired desalination efficiency, water throughput and cost.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Pore‐Scale Modeling of Carbon Dioxide and Hydrogen Transport During Geologic Gas Storage

Abstract Geologic storage of CO 2 and H 2 are climate‐positive techniques for meeting the energy transition. While similar formations could be considered for both gases, the flow dynamics could differ due to differences in their thermophysical properties. We conduct a rigorous pore‐scale study of water/CO 2 and water/H 2 systems at relevant reservoir conditions in a Bentheimer rock sample using the lattice Boltzmann method to quantify the effects of capillary, viscous, inertial, and wetting forces during gas invasion. At similar conditions, H 2 invasion is weaker compared to CO 2 due to unfavorable viscosity ratios. Increasing flow rate, however, increases the breakthrough saturation for both gas systems in the range of capillary numbers studied. At isolated conditions of flow rate, viscosity ratio, and wettability, local inertial effects are found to be critical and show consistent increase in the invaded gas saturation. The effect of inertial forces persits for both gases across all field conditions tested.

58 GEOSCIENCES↗

DOE OSTI2021

Impacts of Pore Network-Scale Wettability Heterogeneity on Immiscible Fluid Displacement: A Micromodel Study

The mixed-wet nature of reservoir formations imposes a wide range of rock wettability from strong resident-fluid wetting to strong invading-fluid wetting. The characteristics of two-phase flow in porous media composed of mixed-wetting surfaces remain poorly understood. In this study, we investigated the displacement of resident ethylene glycol (EG) by hexane in two mixed-wet micromodels of identical 2.5-D geometry heterogeneity, with uniformly or heterogeneously distributed patches strongly wetting to hexane. These patches are mixed among pores with unaltered EG-wetting surfaces. Along with control tests in the originally EG-wet micromodel, here we show the classic fingering and transitions in flow regimes at $logCa$ (capillary number) from -7.2 to -3.9. Moreover, pore-scale distributions of wettability and their spatial correlation influence displacement efficiency. In the two mixed-wet micromodels, we found (a) an increase of steady-state hexane saturation at the end of experiments by up to 0.12 in the capillary fingering regime and a decrease of at most by 0.06 in the viscous fingering regime, compared to the EG-wet micromodel, and (b) dispersed and fragmented hexane distribution after displacement. Brine drainage during supercritical CO 2 (scCO 2 ) injections in these micromodels occurs with lower wettability contrasts, and under similar viscosity ratios and interfacial tensions resulted in higher displacement efficiency relative to displacement of EG by hexane. While mixed-wettability can enhance displacement efficiency compared to uniform wettability, the dynamics of immiscible fluids in strong mixed-wet reservoirs are expected to be less pronounced in contributing to the efficiency of geological CO 2 sequestration, oil recovery, and remediation of hydrocarbon-contaminated aquifers.

2.5-D micromodel↗

DOE OSTI2025

A Multiscale Approach to Simulate Non‐Isothermal Multiphase Flow in Deformable Porous Materials

Coupled thermal, hydraulic, and mechanical processes in porous materials play important roles in several energy and environmental technologies. The Darcy-Brinkman-Biot (DBB) framework has proven effective in modeling multiphase fluid flow in deformable porous solids across both pore and Darcy scales, including in systems where fractures coexist with a porous matrix. In this study, we extend the DBB framework, originally designed for isothermal conditions, to address non-isothermal problems by incorporating an energy conservation equation. The resulting solver, hybridBiotThermalInterFoam, enables simulations of coupled multiphase fluid flow, heat transfer, and solid deformation in hybrid-scale systems containing both solid-free regions and ductile porous domains. The new solver is validated through comparisons with analytical solutions and, also, against established heat transfer solvers chtMultiRegionFoam and compressibleInterFoam. Further, a series of 2D and 3D case studies, including two-phase heat transfer in solid-free, static, or deformable porous media, highlights the solver's capacity to simulate complex flow dynamics and heat transport in systems involving high mobility ratios, viscous fingering, and fracture propagation. Our results establish the feasibility of incorporating thermal effects in simulations of a wide variety of energy geotechnics and environmental applications, including enhanced hydrocarbon recovery, soil remediation, and enhanced geothermal energy systems.

04 OIL SHALES AND TAR SANDS↗

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

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗