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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 OSTI2022

Sodium diffusion in heterogeneous porous media: Connecting laboratory experiments and simulations

Sodium has been suggested as a tracer for brine in reservoir formations where a significant amount of sodium ion is found mainly in the aqueous phase. Fortunately, the most abundant sodium isotope, 23 Na, is Nuclear Magnetic Resonance (NMR) active, making it possible to study the structure and dynamical properties of both bulk and pore confined fluid systems. We investigated the diffusion of key dissolved sodium species in bulk solution and porous media as a function of composition, ionic strength, and permeability of the carbonate samples using NMR relaxometry and pulsed-field gradient (PFG) NMR techniques. We use Indiana limestone as an example of natural porous media and water as a freely diffusible tracer and carrier. We demonstrate apparent diffusion measurement of sodium based on changes in spin–spin relaxation time (T 2 ) signal in pore confinement. The diffusion rate of sodium decreases with increasing counter-ion size. This effect is greater at higher ionic strengths and lower chemical potentials in porous media. The reactive transport code, CrunchFlow, was used to complement the NMR experiments to simulate diffusion behavior in porous media. Combining these two methods provides a powerful approach to estimating effective diffusion coefficients in heterogeneous matrices. The modeling considers the influence of physical properties (porosity and tortuosity) and chemical properties (geochemical composition and chemical gradients). The results presented in this work highlight the advantage of measuring apparent diffusivity using NMR T 2 relaxometry in conjunction with numerical simulation to derive effective diffusivity and the corresponding matrix properties (i.e., tortuosity) of the system.

58 GEOSCIENCES↗

NASA NTRSDate not supplied

Determining Chlamydomonas reinhardtii resistance to ionizing radiation at a genome-wide scale

Spaceflight is a complex mixture of abiotic stresses that causes a myriad of cellular responses including increased genome-wide mutation load. The impact of spaceflight on mutation load is not well understood for most organisms and is especially critical to characterize for candidate microorganisms that could be part of biological life support systems. Prior research in our laboratory revealed an unexpectedly high level of mutation during spaceflight in the eukaryotic green algae, C. reinhardtii. Based on the spectrum of base changes observed, we concluded that the mutations were generated through a molecular mechanism unique to the spaceflight environment. Spaceflight is a complex set of stresses, and we are using an Earth-based analog to test ionizing radiation as a potential causative variable for the unique mutation spectrum observed in spaceflight. C. reinhardtii was grown exposed to chronic radiation from a Cesium-137 source. Four biological replicate cultures of wild-type cells were grown in gas permeable plastic tissue culture bags in liquid media following the design used on the International Space Station (ISS) during the previous space algae experiment. Radiation levels for this experiment approximate ionizing radiation observed on the moon, in low Earth orbit (LEO), and on Earth. Cells from each replicate were passaged to inoculate the next cycle of growth, then samples were taken from each culture to characterize cell morphology, quantify biomass, and extract DNA. Whole genome sequencing from each culture will be used to identify the frequency and types of mutations in each radiation level. In growth cycles 3 and 4, there was a significant increase in biomass accumulation under lunar radiation level compared to LEO or Earth radiation levels. These results such that ionizing radiation affected growth of C. reinhardtii.

Microbiology↗

NASA NTRSDate not supplied

Determining Chlamydomonas Reinhardtii Resistance to Ionizing Radiation at A Genome-Wide Scale

Spaceflight is a complex mixture of abiotic stresses that causes a myriad of cellular responses including increased genome-wide mutation load. The impact of spaceflight on mutation load is not well understood for most organisms and is especially critical to characterize for candidate microorganisms that could be part of biological life support systems. Prior research in our laboratory revealed an unexpectedly high level of mutation during spaceflight in the eukaryotic green algae, C. reinhardtii. Based on the spectrum of base changes observed, we concluded that the mutations were generated through a molecular mechanism unique to the spaceflight environment. Spaceflight is a complex set of stresses, and we are using an Earth-based analog to test ionizing radiation as a potential causative variable for the unique mutation spectrum observed in spaceflight. C. reinhardtii was grown exposed to chronic radiation from a Cesium-137 source. Four biological replicate cultures of wild-type cells were grown in gas permeable plastic tissue culture bags in liquid media following the design used on the International Space Station (ISS) during the previous space algae experiment. Radiation levels for this experiment approximate ionizing radiation observed on the moon, in low Earth orbit (LEO), and on Earth. Cells from each replicate were passaged to inoculate the next cycle of growth, then samples were taken from each culture to characterize cell morphology, quantify biomass, and extract DNA. Whole genome sequencing from each culture will be used to identify the frequency and types of mutations in each radiation level. In growth cycles 3 and 4, there was a significant increase in biomass accumulation under lunar radiation level compared to LEO or Earth radiation levels. These results show that ionizing radiation affected growth of C. reinhardtii.

Hope Hersh↗

DOE OSTI2020

Grain detachment and transport clogging during mineral dissolution in carbonate rocks with permeable grain boundaries

In this paper, we explore the effect of permeable grain boundaries on carbonate rock dissolution in order to improve our understanding of grain detachment and migration during reactive flow. To do so we investigated the effects of grain size and enhanced reactivity along grain boundaries on global dissolution kinetics. Variations of permeability and porosity were calculated, and exponential relationships were observed in fractured rocks. Our model employed a reactive transport framework based on the Darcy-Brinkman equation to simulate calcite dissolution in carbonate rocks composed of microporous grains and, included fluid transport along grain boundaries. The model includes fluid flow, solute transport by advection–diffusion, heterogeneous reaction between fluid and minerals and grain detachment with subsequent grain transport in macropores. The migration of solid particles due to dissolution was based on cluster analysis and local movement, and the results show that grain detachment can lead to significant decreases in permeability due to the clogging of transport pathways. Microporous media with smaller grain sizes (fine grains in this study) showed a higher average reaction rate than those with coarser grains. In addition, as the overall rates of geochemical processes are commonly affected by the presence of texture heterogeneities such as fractures, a single fracture (macropore) introduced into a microporous matrix composed of permeable grains and grain boundaries was modelled as a large channel connecting the inlet and outlet of the simulation domain. It was found that macropore clogging by grain detachment temporary decreased permeability, lowering the long-term global reaction rates. Lastly, we observed that increases in flow rate can reduce detachment and fracture clogging by reducing local dissolution along grain boundaries.

58 GEOSCIENCES↗

NASA NTRS1984

Separator plugs for liquid helium

Work performed during Summer 1984 (from June to Sept. 30) in the area of porous media for use in low temperature applications is discussed. Recent applications are in the area of vapor - liquid phase separation, pumping based on the fountain effect and related subsystems. Areas of potential applications of the latter are outlined in supplementary work. Experimental data have been developed. The linear equations of the two-fluid model are inspected critically in the light of forced convection evidence reported recently. It is emphasized that the Darcy permeability is a unique throughput quantity in the porous media application areas whose use will permit meaningful comparisons of data not only in one lab but also within a group of labs doing porous plug studies.

Lee, J. M.↗

DOE OSTI2022

Macrovoid resolved simulations of transport through HPRO relevant membrane geometries

Modeling the transport properties such as diffusivity and permeability of high pressure reverse osmosis (HPRO) membranes is critical for the selection and manufacture of membranes suitable for operation under high pressure. These properties can be significantly affected by the changes in heterogeneous pore structures due to compaction. Here, the modeling platform presented in this work resolves the two scale porosity in HPRO relevant membranes. A synthetic membrane geometry is constructed based on available experimental visualizations of pore structures. The simulations directly capture the flow channeling that results from a combination of material properties and geometric features of the macrovoids. A parametric study is presented to account for the transition of flow characteristics from a material governed regime to a macrovoid governed regime. Permeability of the membrane is evaluated using the simulation data and compared with an existing model that scales with the square of tortuosity over a range of material properties. The model is found to perform well under a narrow range of tortuosity while deviating from the calculated permeabilities at extreme conditions. The effective permeability of the membrane is found to vary by at least two orders of magnitude between the two flow regimes. It is also observed that tortuosity is a bounded property with its upper limit determined by the macrovoid geometry. Consequently, the tortuosity based correlations fail near a flow regime that is mainly governed by the macrovoids. The modeled permeability can be more than an order of magnitude smaller than the simulation result. A new model based on flux-weighted porosity of a membrane is introduced and its correlation with tortuosity is studied. The model agrees with the simulated data as, in addition to tortuosity, it also accounts for the flux partition within and outside the flow channels. Such correlations enable extending the existing understanding of flow characteristics to enhance predictability of porous media models.

42 ENGINEERING↗

DOE OSTI2020

Three-Dimensional Imaging and Quantification of Gas Storativity in Nanoporous Media via X-rays Computed Tomography

This study provides the engineering science underpinnings for improved characterization and quantification of the interplay of gases with kerogen and minerals in shale. Natural nanoporous media such as shale (i.e., mudstone) often present with low permeability and dual porosity, making them difficult to characterize given the complex structural and chemical features across multiple scales. These structures give nanoporous solids a large surface area for gas to sorb. In oil and gas applications, full understanding of these media and their sorption characteristics are critical for evaluating gas reserves, flow, and storage for enhanced recovery and CO 2 sequestration potential. Other applications include CO 2 capture from industrial plants, hydrogen storage on sorbent surfaces, and heterogeneous catalysis in ammonia synthesis. Therefore, high-resolution experimental procedures are demanded to better understand the gas–solid behavior. In this study, CT imaging was applied on the sub-millimeter scale to shale samples (Eagle Ford and Wolfcamp) to improve quantitative agreement between CT-derived and pulse decay (mass balance) derived results. Improved CT imaging formulations are presented that better match mass balance results, highlighting the significance of gas sorption in complex nanoporous media. The proposed CT routine implemented on the Eagle Ford sample demonstrated a 17% error reduction (22% to 5%) when compared to the conventional CT procedure. These observations are consistent in the Wolfcamp sample, emphasizing the reliability of this technique for broader implementation of digital adsorption studies in nanoporous geomaterials.

42 ENGINEERING↗

DOE OSTI2025

Permeability Prediction Using Vision Transformers

Accurate permeability predictions remain pivotal for understanding fluid flow in porous media, influencing crucial operations across petroleum engineering, hydrogeology, and related fields. Traditional approaches, while robust, often grapple with the inherent heterogeneity of reservoir rocks. With the advent of deep learning, convolutional neural networks (CNNs) have emerged as potent tools in image-based permeability estimation, capitalizing on micro-CT scans and digital rock imagery. This paper introduces a novel paradigm, employing vision transformers (ViTs)—a recent advancement in computer vision—for this crucial task. ViTs, which segment images into fixed-sized patches and process them through transformer architectures, present a promising alternative to CNNs. We present a methodology for implementing ViTs for permeability prediction, its results on diverse rock samples, and a comparison against conventional CNNs. The prediction results suggest that, with adequate training data, ViTs can match or surpass the predictive accuracy of CNNs, especially in rocks exhibiting significant heterogeneity. This study underscores the potential of ViTs as an innovative tool in permeability prediction, paving the way for further research and integration into mainstream reservoir characterization workflows.

58 GEOSCIENCES↗

DOE OSTI2023

Effect of Formation Heterogeneity on CO 2 Dissolution in Subsurface Porous Media

Dissolution trapping is one of the most dominant mechanisms for the secure storage of CO 2 injected in porous subsurface formations saturated with brine. This trapping mechanism is enhanced by convective mixing, which occurs due to the gravitational instability between the different fluid layers in the aquifer. The reservoir permeability also plays a crucial role in the dissolution rate and overall fluid flow dynamics during the density-driven convection in porous media. Herein this study investigates the role of complex heterogeneity, i.e., irregular permeability distribution in CO 2 dissolution, using a novel experimental approach to create medium permeability heterogeneity in Hele–Shaw cells. Complex subsurface transport phenomena such as a preferential dissolution path, CO 2 sweep efficiency, changes in finger morphology, and CO 2 concentration distribution are visualized by creating heterogeneous media. Experimental results showed that reservoir permeability heterogeneity causes significant channeling effects and poor sweep efficiency. A scaling relationship between average finger growth rate (Gr) and permeability (k) was obtained as Gr [m s –1 ] = 266.8k [m 2 ] + 1.20 × 10 –6 . Furthermore, the mass of CO 2 dissolved is calculated using the spectrophotometric method to characterize the convective instability. The convective flux was analyzed by comparing the experimental dissolution flux with the theoretical diffusion flux, calculating a maximum Sherwood number of 6.8. The study’s findings improve the current understanding of the CO 2 convection morphology in heterogeneous media, allowing better assessment of long-term CO 2 storage.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Quantifying the Effect of Pore‐Size Dependent Wettability on Relative Permeabilities Using Lattice Boltzmann Simulation

Relative permeability is a crucial two-phase property in porous media that can be significantly impacted by wettability conditions. While traditional research has predominantly examined homogeneous wettability, this work explores the less studied pore-size dependent (PSD) wettability, featured by a pore-size dependent wettability distribution. Leveraging high-fidelity Lattice Boltzmann simulations on CT-scanned porous samples, we demonstrate how PSD wettability would impact relative permeability at the pore scale. Our findings reveal that the deviation of relative permeability from the homogeneous wettabilitity induced by PSD wettability can be 5%–20%. The deviation of relative permeability curves increases as the spanning range of the contact angle increases. We also find that this impact is less pronounced as the capillary number increases. By adopting a pore-size-dependent contact angle relationship, our approach provides a more accurate and nuanced understanding of how PSD wettability would impact two-phase flow. These findings discovered at the pore scale may also provide valuable insights on relative permeability at the core to reservoir scales.

25 ENERGY STORAGE↗

DOE OSTI2020

τ-SIMPLE Algorithm for the closure problem in homogenization of stokes flows

Estimation of the permeability tensor is crucial for many natural and industrial porous media applications. Homogenization provides a rigorous framework to calculate effective parameters from pore-scale images of a representative unit cell of the porous medium by solving a boundary value problem, also known as closure problem, subject to global constraints. However, the latter are hard to satisfy for arbitrarily complex geometries. We have developed a novel computational algorithm to calculate rigorously the permeability tensor. The approach, here referred to as τ-SIMPLE, is based on introducing an artificial time scale τ to satisfy the global constraint within the SIMPLE iteration. Here, we show that the proposed algorithm has high accuracy for both two-dimensional and three-dimensional periodically arranged geometries.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

The impact of mineral reactive surface area variation on simulated mineral reactions and reaction rates

Reactive transport modeling is an essential tool to simulate complex geochemical reactions in porous media that can impact formation properties including porosity and permeability. However, simulating these reactions is challenging due to uncertainties in model parameters, particularly mineral surface areas. Imaging has emerged as a powerful means of estimating model parameters including porosity and mineral abundance, accessibility and accessible surface area. However, these parameters, particularly mineral accessible surface area, vary with image resolution. This work aims to enhance understanding of the impact of image resolution and other means of estimating mineral reactive surface area on simulated mineral reactions and reaction rates. Mineral surface areas calculated from images with resolutions of 0.34 μm and 5.71 μm were used to simulate mineral reactions in the context of geologic CO 2 sequestration in the Paluxy formation at the continuum scale. Additional simulations were carried out using BET surface areas collected from the literature and geometric surface areas. Simulations were run for 7300 days and mineral volume fractions and effluent ion concentrations tracked and compared. Variations in mineral surface areas measured from images are within 1 order of magnitude and yield similar simulation results, indicating the impact of image resolution on simulated reactions and reaction rates is minimum for the resolutions and sample considered. In comparison, surface areas obtained from BET and geometric approaches are 1–4 orders of magnitude higher than image-obtained surface areas and result in greater simulated reaction rates and extents. Minerals with high reaction rates (calcite and siderite) are most impacted by surface area values at short times where simulated mineral volume fractions at longer times agree relatively well, even for simulations with several orders of magnitude variation in surface area. Phases with lower reaction rates, such as K-feldspar and muscovite, are predominantly impacted over longer times where variations in surface areas impact reaction extents and porosity evolution. Overall, variations in surface areas due to image resolution are small and result in little variation in simulated reactions and reaction rates while there are significant variations in simulation results when other surface area estimates are used. These variations, however, depend on the reactivity of the mineral phase where surface areas of fast-reacting phases largely impact simulations at short (hours to days) timescales and surface areas of slower-reactive phases impact longer term simulations (years).

58 GEOSCIENCES↗

DOE OSTI2023

Tetrapodal textured Janus textiles for accessible menstrual health

Menstruating individuals without access to adequate hygiene products often improvise with alternatives that pose health risks and limit their participation in society. We describe here a menstrual hygiene product based on low-cost materials, which are integrated onto fabrics to imbue unidirectional permeability. A body-facing "Janus" fabric top layer comprising ZnO tetrapods spray-coated onto polyester mosquito netting imparts hierarchical texturation, augmenting the micron-scale texturation derived from the weave of the underlying fabric. The asymmetric coating establishes a gradient in wettability, which underpins flash spreading and unidirectional permeability. The hygiene product accommodates a variety of absorptive media, which are sandwiched between the Janus layer and a second outward-facing coated densely woven fabric. An assembled prototype demonstrates outstanding ability to wick saline solutions and a menstrual fluid simulant while outperforming a variety of commercially alternatives. The results demonstrate a versatile menstrual health product that provides a combination of dryness, discretion, washability, and safety.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1989

Critical transport parameters for porous media subjected to counterflow

Experimental and theoretical studies have been conducted to determine critical parameters at the onset of nonlinear counterflow in He II below the lambda point of He-4. Critical temperature differences have been measured in porous media for zero net mass flow and for Darcy permeabilities in the order of magnitude range from 10 to the -10th to 10 to the -8th sq cm. The normalized critical temperature gradients, which covered the liquid temperature range of 1.5 K to the lambda temperature, are found to vary with T proportional to the ratio of the superfluid density to the normal fluid density. This liquid temperature dependence appears to be consistent with duct data which are limited at low temperature by a Reynolds number criterion.

Frederking, T. H. K.↗

DOE OSTI2022

Dynamic three-dimensional maps of solute concentration and solute arrival times in synthetic and geologic porous media

Experimental and training data associated with the publication entitled ‘Three-Dimensional Permeability Inversion Using Convolutional Neural Networks and Positron Emission Tomography’ (published in WRR, DOI: 10.1029/2021WR031554). The dataset contain three-dimensional maps of various properties on four geologic rock cores obtained from X-ray Computed Tomography and Positron Emission Tomography imaging measurements. The synthetic training dataset used in the publication is also attached.

58 GEOSCIENCES↗

DOE OSTI2020

Improved pore network models to simulate single-phase flow in porous media by coupling with lattice Boltzmann method

In this paper, different pore network models to simulate single-phase flow in porous media are built and their accuracy is evaluated. In addition to the conventional pore network model (CPNM) which consists of regular pore bodies and throat bonds, three improved pore network models (IPNMs) are developed allowing to better describing the real pore and throat geometry. The first improved pore network model (IPNM1) replaces the regular throat bond with a throat bond showing the real throat cross section. The second improvement (IPNM2) uses a series of sub-throat bonds with varying cross sections to better describe the real throat geometry, which is firstly proposed in this paper. The third model (IPNM3) extracts the real pore-throat-pore geometry without simplification. The conductance of fluid flow through these more realistic throat bonds is calculated by the lattice Boltzmann method (LBM). The accuracy and computational efficiency of the different pore network models are evaluated taking the LBM simulation over the whole porous medium as reference solution. The global permeability and detailed pressure distributions in the pores for the different pore network models are validated. The results show that the accuracy of the pore network model increases from CPNM to IPNM3, but at the expense of increasing computational cost. This study suggests that IPNM3 can replace a whole-domain LBM simulation with similar accuracy but much lower computational cost. As a first-order approximation the newly proposed IPNM2 is suggested as good compromise between accuracy and computational cost.

42 ENGINEERING↗

DOE OSTI2024

Fast permeability measurement for tight reservoir cores using only initial data of the one chamber pressure pulse decay test

Here, in this study, a mathematical model for fast determination of the permeabilities of tight rocks using measurements taken from the initial period of the One Chamber Pressure Pulse Decay (OC-PPD) test is presented. The model applies to measurements taken both before and after the pressure pulse front has reached the downstream end of the specimen. The analytical solutions for the pressure decay in the upstream chamber are derived based on a parabolic arc approximation of pore pressure distribution along the test specimen. This approximation allows converting the initial–boundary value problem of fluid diffusion in the specimen, governed by partial differential equations, to a system of ordinary differential equations that can be easily solved by explicit formulae. Thus, an explicit formula for the pressure decay rate is obtained, which enables inverse analysis of the initial experimental data to estimate the rock permeability. The proposed method expedites the pulse decay test as it does not require the system to reach equilibrium. The method is validated with three sets of experimental data of the OC-PPD test using helium as the diffusing fluid, for which the relative error of the permeability is found to be less than 6%. This method is particularly useful if the equilibrium time of the pulse decay test for rock specimens with permeabilities in the range of nano-Darcy takes hours or days.

early-time solution↗