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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Estimation of extreme temperatures in direct solar methane pyrolysis within a porous medium

Porous media have wide application in renewable energy conversion processes, such as solar-thermal fuels production and decarbonization. Heat transport mechanisms within porous media can be highly complex, particularly under extreme conditions encountered in concentrated solar thermal reactors in which direct measurement of temperature is challenging. Here, we implement and report an inverse heat conduction model to estimate the temperature distribution throughout a porous substrate domain in a direct solar methane pyrolysis process. By solving a two-dimensional heat transfer problem and applying an inverse optimization algorithm, we estimate the quasi-steady state spatial temperature distribution in a fibrous porous carbon substrate. The results are validated indirectly by experimentally measured graphite deposition and a simplified reaction kinetic model.

finite difference method↗
DOE OSTI2025

Fluid/Fluid Interfacial Areas Measured for Different Non-Wetting/Wetting Fluid Pairs in Natural Porous Media

This study examined the impact of fluid type and grain diameter on the interfacial area between different pairs of non-wetting and wetting fluids in natural porous media. Synchrotron X-ray microtomography was used to obtain high-resolution, three-dimensional images of multi-phase porous media systems. Multiple porous media, comprising a range of physical and geochemical properties, were used in this study. The four pairs of non-wetting/wetting fluids used were dense OIL/water, light OIL/water, air/dense OIL, and air/water. Images were obtained over a broad range of wetting phase saturation and for both wetting phase drainage and imbibition conditions. The results showed that for each fluid pair, the total (capillary + film) interfacial area increased with decreasing wetting fluid saturation. Interfacial areas were similar among all fluid pairs for a given porous medium. They were also similar for drainage and imbibition conditions. The maximum specific interfacial area (A m ) was shown to correlate well with inverse median grain diameter. The physical properties of the porous medium appear to have a greater influence on the magnitude of specific total interfacial area for a given saturation than fluid properties or wetting phase history.

NAPL↗
DOE OSTI2023

MOOSE Navier–Stokes module

The MOOSE Navier–Stokes module solves mass, momentum, energy, and passive scalar conservation equations in the context of fluid flow. The module supports solution of these equations in both free flow and porous medium contexts and for a range of fluid compressibility. The conservation equations can be discretized in space using continuous Galerkin finite elements or with cell centered finite volumes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Pore-Scale Study on the Positive Feedback Between Stress and Porosity Caused by Pressure Solution in Porous Media

Pressure solution is an important process in the evolution of sedimentary rocks, which provide storage space for most of our petroleum resources. It directly influences the generation, migration, and storage of petroleum fluids in subsurface sedimentary rocks. Here, in this paper, we develop a pore-scale, mechanochemical model to demonstrate a possible positive feedback between the local porosity and pore surface stress, in which a higher local porosity causes a higher local pore surface stress, thus enhancing pressure solution and consequently further increasing the local porosity. Pore surface stress represents stress on a solid grain adjacent to a pore. Specifically, the pore-scale, mechanochemical model directly simulates the stress distribution over solid and pore surfaces using a finite element model. The dissolution of solids at the solid-pore interfaces under a far-from-equilibrium condition is simulated using a first-order kinetics model that accounts for the local stress distribution. The updated pore geometry, caused by pore surface dissolution, is then used in the stress simulation in the next numerical iteration. Two types of porous media, the Oriskany sandstone and an artificial porous medium with spherical pores, were tested in the mechanochemical simulation. The positive stress-porosity feedback during pressure solution was observed in both samples. In addition, the model quantitatively illustrated the distribution of local mineral dissolution rates on all pore surfaces, as well as its relation to the effective mineral dissolution rate of the entire sample. Based on the comparison between the two porous media, the local mineral dissolution was regulated by pore space distribution, geometry, and coalescence during pressure solution. This work is the first that uses direct, pore-scale numerical simulation to demonstrate the positive stress-porosity feedback during pressure solution, which has the potential to advance the understanding of the mechanical-chemical (MC) coupling in many geological processes that are relevant to subsurface energy systems, such as the recovery of petroleum hydrocarbons and geothermal energy.

CT scanning↗
DOE OSTI2026

Enhanced Manganese Oxidation at the Biofilm–Fluid Interface Drives Pore-Scale Patterns in Mineral Precipitation

Microbial oxidation of manganese (Mn) from aqueous Mn(II) to solid-phase Mn(III, IV) minerals catalyzes Mn(II) removal in natural and engineered porous systems. However, little is known about the spatiotemporal evolution of Mn biomineralization in confined spaces that experience simultaneous Mn(II) delivery and Mn oxide precipitation. Here, we combine time-lapse microscopy, image analysis, and mass spectrometry to quantify the extent and rate of Mn biomineralization by Pseudomonas putida GB-1 in an optically transparent two-dimensional porous medium. We found that Mn(II) oxidation initially occurred within biofilms but shifted over time toward the edges of biofilms in contact with pore fluid. Minerals precipitated outside of the initial biofilm footprint likely due to surface-mediated oxidation of Mn(II) by nascent biogenic Mn oxides, reinforcing a gradient in mineral accumulation from the Mn(II) source near the reactor inlet to the outlet. The rate of mineral precipitation outside the biofilm footprint surpassed the rate of mineral accumulation inside biofilms within 6 h and accounted for two-thirds of the total Mn oxide mass in the pore space at the end of the experiment. This work advances a mechanistic understanding of coupled biotic and abiotic Mn oxidation in porous environments while providing a novel platform to quantify microbe-mineral-fluid interactions.

Biofilms↗
DOE OSTI2025

Discrete fracture network model benchmarks developed and applied in a DECOVALEX-2023 repository performance assessment study

This study presents newly developed benchmarks for modeling flow and transport within discrete fracture networks (DFNs) and useful methods for analyzing the results. The new benchmarks are designed to test modeling approaches for use in probabilistic performance assessment models of deep geologic repositories in fractured rock. The benchmarks simulate flow and transport through a 1 km 3 block of fractured rock. The first simulates migration of a short pulse of tracer through a simple network of four intersecting fractures. The second adds 1089 stochastically generated fractures. The third changes the pulse to a continuous point source. Evaluation of model performance relies on moment analysis and comparison of the results of different models. The expected nondimensional first moment of the conservative tracer for each benchmark is 1. The benchmarks were simulated by teams from Canada, Czechia, Germany, Korea, Sweden, Taiwan, and the United States as part of a DECOVALEX-2023 study (decovalex.org). The teams used various approaches, including explicit DFN modeling, DFN upscaling to an equivalent continuous porous medium (ECPM), and a combination of both methods. Transport mechanisms are modeled using either the advection-dispersion equation or particle tracking. Results demonstrate strong agreement among the models in breakthrough behavior up to the 75th percentile. Significant deviations in first moments and well-clustered outputs led to the identification of inaccuracies in several models. Such findings exemplify the benefit of exercising these benchmarks and using the presented methods to test DFN flow and transport models.

Benchmark↗
DOE OSTI2025

A simplified CFD approach for modeling mass transport in catalytic open-cell foams

A simplified macroscopic CFD approach is presented to model mass transport including chemical reactions in washcoated open-cell foams. The foam is treated as a porous medium. Species conversion during chemical reactions is modeled using appropriate source terms based on reaction rate expressions and modified to account for the mass transport resistances occurring at the fluid-washcoat interfaces and within the washcoat layers. As example, the catalytic CO oxidation over platinum is studied. The simulation results show good agreement with experimental data from literature. A parametric study on washcoat parameters, such as thickness, tortuosity, porosity, and size, is carried out. Increasing the washcoat thickness from 5 to 100 µm or decreasing the tortuosity to porosity ratio from 5 to 20 decreases the CO conversion by 10 %. The proposed model is found to be reliable and has the advantage of lower computational cost, making it a suitable tool for foam-based catalytic reactor design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Simulations of flaming combustion and flaming-to-smoldering transition in wildland fire spread at flame scale

Our objective in the present study is to provide basic insights into the coupling between external-gas and solid biomass vegetation processes that control the dynamics of flame spread in wildland fire problems. Here we focus on a modeling approach that resolves processes occurring at vegetation and flame scales, i.e., the formation of flammable vapors due to the thermal degradation of the solid biomass, the subsequent combustion in ambient air, the thermal feedback to the biomass through radiative and convective heat transfer, and the possible transition from flaming combustion (taking place outside of the solid biomass) to smoldering combustion (taking place inside the solid biomass). The capability uses a multiphase combustion framework and treats external-gas processes through a Large Eddy Simulation solver and solid biomass processes through a discrete particle model. The discrete particle model adopts a one-dimensional porous medium formulation, includes descriptions of drying, thermal pyrolysis, oxidative pyrolysis, and char oxidation, as well as a description of the external-gas-to-solid-biomass diffusion of oxygen mass; the discrete particle model thereby provides a treatment of in-depth oxidative processes and allows the simulation of smoldering combustion. The modeling capability is applied to the simulation of fire spread across a surrogate biomass vegetation bed corresponding to a discrete array of cylindrical-shaped, vertically-oriented, pine wood sticks, characterized by a monomodal size distribution, in horizontal flat terrain and under wind-aided conditions. The numerical results demonstrate that the model can simulate successful flaming-to-smoldering transition followed by complete biomass consumption.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2023

Methane mass transfer in mesoporous silica saturated with liquid hydrocarbons

Mass transfer across gas/liquid interfaces plays a central role in many industrial applications. In particular, gas dissolution and diffusion in liquid hydrocarbon mixtures, confined in nanometer-sized pores, is an essential mechanism during enhanced oil recovery (EOR) from unconventional formations. In this work, we have measured methane (C 1 ) diffusion in n-decane (C 10 ), n-hexadecane (C 16 ), and mixtures of C 10 + C 16 in a mesoporous material with an average pore size of 4 nm at 50 °C and ~ 8 MPa of gas pressure. A key conclusion of this work is that the diffusivities, measured in the bulk phase, for the relevant binary systems, are sufficient to predict the diffusion behavior of the corresponding multicomponent systems in the porous medium by using Wilke’s equation for the evaluation of effective component diffusivities, combined with an accurate equation of state (EOS) representation of the (bulk) phase behavior. This observation can facilitate accurate prediction of recovery processes in unconventional formations and, potentially, guide other applications that entail gas-liquid interface mass transfer in mesoporous materials.

42 ENGINEERING↗
DOE OSTI2025

Characterizing the pore-scale impacts of enhanced-solubilization solutions on organic-liquid morphology and fluid-fluid interfacial area with microtomography

Synchrotron X-ray microtomography was used to directly quantify the impact of enhanced-solubilization solutions on mobilization of a non-wetting fluid in a natural porous medium. Polyoxyethylene sorbitan monooleate (tween 80), hydroxypropyl-β-cyclodextrin (HPCD), sodium dodecyl sulfate (SDS), and ethanol were used as the solubilization reagents. Tetrachloroethene (PCE) was used as the entrapped organic immiscible liquid. Microtomography images were collected prior to and after successive floods with each reagent solution. The total trapping number was varied by more than three orders of magnitude by changing the velocity and viscosity of the aqueous phase as well as the interfacial tension between fluid phases. The results were compared to those obtained from equivalent experiments conducted with water flooding. Inspection of images indicated that mobilization caused a change in PCE morphology and distribution for all reagents with the exception of HPCD, for which a lower trapping number was determined compared to the other experiments. Mobilization of organic liquid was observed at total trapping numbers that were consistent with prior work. The enhanced-solubilization solutions had minimal impact on the configuration or magnitude of fluid-fluid interfacial area.

Interfacial area↗
DOE OSTI2024

Containment strategy for subsurface H 2 storage based on time-dependent soft solids

Here, we propose an innovative containment strategy based on time-dependent soft solids, namely 2 wt% Laponite suspensions, to reinforce natural subsurface seals and engineer flow barriers, with an eye toward making H 2 subsurface storage scalable and geographically agnostic. This suspension can be injected at its initial low viscosity and elasticity into a porous medium, allowing for easy pumping and targeted delivery. Once inside the target zone, it matures into a soft solid with much higher viscosity and elasticity, acting as a potential flow barrier. We discuss the rheological properties of the suspensions and demonstrate that hydrogen does not adversely affect their microstructure, but rather increases the suspensions’ viscosity and elasticity. Moreover, the suspensions enhance the rock samples’ compressive strength, while hydrogen exposure increases their stiffness and ductility. The ability of rock samples saturated with the suspensions to contain higher injected gas pressures is enhanced by aging at higher temperatures.

08 HYDROGEN↗
DOE OSTI2025

Experimental observation of nonlinear relation between pressure and water flux is consistent with the solution-diffusion model

In several recent studies, it has been proposed that the fundamental understanding of penetrant transport in dense polymer membranes occurring via the solution-diffusion model, which has been the generally accepted theoretical framework for describing penetrant transport in such materials for the past several decades, is flawed. An alternate mechanistic framework based on the idea of two-phase flow in a porous medium (i.e., pore-flow) has been broadly advanced instead, with proponents of this approach claiming that the pore-flow theoretical framework provides the necessary mechanistic insight to design novel polymeric membrane materials for emerging applications. In this study, we show experimental results for hydraulic permeation of water that are entirely consistent with the solution-diffusion theory, without modification, for three dense polymeric membranes: crosslinked poly(ethylene glycol diacrylate) (XLPEGDA), Nafion 117 ionomer in the sodium counterion form (Nafion 117-Na), and cellulose acetate (CA). By measuring water flux at transmembrane pressures up to 240 bar, we observe a nonlinear relationship between the transmembrane pressure (TMP) and water flux, J w , for XLPEGDA and Nafion 117-Na, while this relationship is linear for CA. We demonstrate that the behavior of these three materials is described via the solution-diffusion model. According to the solution-diffusion model, flux is, to a good approximation, proportional to the transmembrane concentration difference induced by the pressure difference across the membrane, rather than to TMP itself. Water sorption isotherms are reported for all three materials. They further justify the nonlinear relationship between TMP and J w observed in XLPEGDA and Nafion 117-Na, emphasizing that the nonlinearity in the flux/TMP relationship stems from nonlinearities in the sorption isotherm with pressure. Additionally, the relationship between water flux and TMP can be predicted, a priori, with no adjustable parameters when a predictive model for the diffusion coefficient of water is employed in conjunction with the experimental water sorption isotherms in the solution-diffusion model. Furthermore, our results demonstrate the validity of the solution-diffusion model to describe transport of penetrants in dense polymer membranes, while highlighting the sensitivity of the solution-diffusion model to the many physical and mathematical simplifications commonly applied to the theory in literature.

materials↗
DOE OSTI2023

Redox-Based Chemical Looping Large-Scale Air Separation Unit Designs Using Perovskite Material

Oxygen production by means of air separation through redox cycle reactions of Sr 1–x Ca x FeO 3-δ perovskite particles is examined numerically in the context of modular large-scale units. Fixed-bed, multicomponent reactor designs allowing for the recovery of the energy released by the exothermic oxidation (or adsorption) to enhance the endothermic reduction (or desorption) of the perovskite material are considered and compared against a baseline cylindrical packed bed. Numerically, the gas–solid reacting system is approximated as a single-phase reacting gas flow through a porous medium of constant porosity. The redox kinetics account for the oxygen nonstoichiometry of the perovskite, which exhibits a dependence on the temperature and the oxygen partial pressure, in order to describe some mechanisms of the oxygen vacancies. Results show that the spontaneous release of the oxygen from the lattice arrangements, through the thermal management of the heat of the oxidation reaction from the geometrical design of the reactors, can be enhanced up to 4% with respect to the baseline oxygen production of 0.201 g O 2 ·h –1 ·g perovskite –1 with the cylindrical packed bed, in the condition of operations in this work, at 500 °C. Sensitivity to the operation temperature showed that the oxygen production is greatly enhanced by approximately 30% with the increase of the temperature from 500 to 550 °C. We report this result is consistent with experimental observations of faster release of the oxygen from the lattice arrangements of this perovskite at 550 °C.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Modeling Geologic Waste Repository Systems Below Residual Saturation

The heat generated by high-level radioactive waste can pose numerical and physical challenges to subsurface flow and transport simulators if the liquid water content in a region near the waste package approaches residual saturation due to evaporation. Here, residual saturation is the fraction of the pore space occupied by liquid water when the hydraulic connectivity through a porous medium is lost, preventing the flow of liquid water. While conventional capillary pressure models represent residual saturation using asymptotically large values of capillary pressure, here, residual saturation is effectively modeled as a tortuosity effect alone. Treating the residual fluid as primarily dead-end pores and adsorbed films, relative permeability is independent of capillary pressure below residual saturation. To test this approach, PFLOTRAN is then used to simulate thermal-hydrological conditions resulting from direct disposal of a dual-purpose canister in unsaturated alluvium using both conventional asymptotic and revised, smooth models. Importantly, while the two models have comparable results over 100 000 years, the number of flow steps required is reduced by approximately 94%.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Multiphysics modelling in PyLith: poroelasticity

SUMMARY PyLith, a community, open-source code for modelling quasi-static and dynamic crustal deformation with an emphasis on earthquake faulting, has recently been updated with a flexible multiphysics implementation. We demonstrate the versatility of the multiphysics implementation by extending the code to model fully coupled continuum poromechanics. We verify the newly incorporated physics using standard benchmarks for a porous medium saturated with a slightly compressible fluid. The benchmarks include the 1-D consolidation problem as outlined by Terzaghi, Mandel’s problem for the 2-D case, and Cryer’s problem for the 3-D case. All three benchmarks have been added to the PyLith continuous integration test suite. We compare the closed form analytical solution for each benchmark against solutions generated by our updated code, and lastly, demonstrate that the poroelastic material formulation may be used alongside the existing fault implementation in PyLith.

Geochemistry & Geophysics↗
DOE OSTI2024

DECOVALEX-2023: Task F1 Final Report

DECOVALEX-2023 Task F is a comparison of models and methods for post-closure performance assessment (PA) of a deep geologic repository for radioactive waste. The general aims of Task F are to build confidence in the models, methods, and software used for PA and to stimulate additional research and development in PA methodologies. The task objectives are to motivate development of PA modelling skills and capabilities, to examine the influence of model choices on calculated repository performance, and to compare the uncertainties introduced by model choices to other sources of uncertainty. Task F involves no actual experiment or site. It is a PA modelling exercise that requires the conceptual development of hypothetical repository designs and geologic settings. Because three of the teams were interested in salt and the rest of the teams were interested in crystalline rock, Task F was split into two branches: Task F1 for crystalline rock and Task F2 for salt. This report is for Task F1, crystalline rock. Teams from seven countries (Canada, Czech Republic, Germany, Korea, Sweden, Taiwan, and United States) participated in Task F1. The teams worked together to define the features, events, and processes of the reference case repository and established a set of performance measures. In addition, they defined a set of benchmark problems designed to test and compare modelling capabilities for fracture flow and transport at different scales. The repository design and benchmark problems are documented in a Task Specification that evolved over time as the group honed the specifications. The benchmark problems verified that each team can aptly model flow and transport in fractured media in 1-, 2-, and 3-dimensions. Two general approaches were used for the 3-dimensional benchmarks: discrete fracture network (DFN) and equivalent continuous porous medium (ECPM). DFN modelling involves explicit meshing of each fracture while ECPM modelling aims to capture the effective porosity and directional permeability of each cell in a space-filling mesh as affected by intersecting fractures. In some models, a combination of the two is used, i.e., DFN for large known fractures and ECPM for the rest of the domain. Transport is solved by using either the advection-dispersion equation or particle tracking. Although some variation is observed among model breakthrough curves in the benchmark problems, there is strong agreement in breakthrough behaviour up to at least the 75 th percentile for all benchmarks. At the 90 th percentile, breakthrough results show larger differences, suggesting several models retain substantially higher fractions of tracer in regions of slower moving water. In addition to the flow and transport benchmarks, several teams completed the source term benchmark, verifying capabilities for modelling radionuclide decay and ingrowth, waste package breach, instant release fractions, fuel matrix degradation rates, and radionuclide solubility limitations. The reference case is conceptualized as a generic spent fuel repository at a depth of 450 m in fractured crystalline rock. The repository has 50 parallel backfilled drifts, each with 50 deposition holes 6 m apart. Each deposition hole contains a 4-PWR waste package and bentonite buffer. The rock domain is 5 km in length, 2 km in width, and 1 km in depth. It has 6 deterministic fractured deformation zones and a multitude of stochastic fractures. Teams generally used the ECPM approach for the entire rock or a hybrid approach in which the deterministic fracture zones are modelled with a DFN and the rest of the rock is modelled by ECPM. Of the reference case problems specified, only the results of the initial reference case problem are compared in this report. The initial problem focuses on transport from the deposition holes to the surface, i.e., it neglects waste package performance. Tracers are released at all waste package locations at time zero and tracked for their releases to the near field and ground surface. The water fluxes calculated at the ground surface entry and exit regions of the domain are similar for all models except for two that have considerably lower fluxes. For tracer transport, large differences are observed among models in the magnitude of tracer transported. Much of the difference appears to be due to how the repository is implemented and hence the different degrees of repository simplification. Models that exclude the drifts, buffer, and backfill from the domain tend to show greater release of tracers and radionuclides from the repository. The initial study presented here indicates that major differences in modelling important processes within the repository (e.g., diffusion through buffer and backfill) can produce broadly different release and transport results, especially when those processes are excluded. Even for the models that included all specified features, events, and processes, the results show significant differences and demonstrate the importance of examining multiple modelling approaches in performance assessment. The differences in results observed in this study are expected to motivate teams to either increase complexity in future versions of the reference case models or to improve methods to account for the effects of simplified features and processes. Either way, future improvements in these models are expected to produce results that more closely agree.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Towards a Unified Low-Cost Flow Plate, Flow-Field, PTL Solution for Proton Exchange Membrane Electrolyzers

Proton exchange membrane (PEM) water electrolysis is a highly efficient method for hydrogen production. Research cells typically consist of one proton exchange membrane, two catalyst layers, two porous transport layers, two flow-field plates, and two endplates. In commercial systems, the machined flow-field plates that are employed in research cells are typically replaced by stamped parts or open mesh material solutions to reduce manufacturing cost at scale. Nonetheless, the cell contains about 8 total interfaces: bipolar plate / flow plate material / porous transport medium / electrode / membrane / electrode / porous transport medium / flow plate material / bipolar plate. All these materials and interfaces need to be optimized for maximum performance and efficiency. Reducing the amount of interfaces by combining individual cell components directly benefits the fabrication cost (by reducing the parts count and the needs for surface coatings) and the electrochemical performance (by reducing ohmic losses). We have designed a novel PEM electrolysis cell with a piece of channeled titanium felt functioning as both the anode flow-field and the PTL, referred to as the channeled diffusion layer (CDL). The pores of the felt facilitate both in-plane and through-plane diffusion, ensuring maximum catalyst utilization while also minimizing mass transport loss. The titanium felt can be mass manufactured with existing stamping and forming methods and is therefore a promising candidate to reduce the capital cost of PEM electrolyzers whilst improving hydrogen production efficiency. Experiments conducted with 3mg IrOx/cm2 loading MEAs have shown a approximately 40% boost in peak current by implementing the CDL design. Low catalyst-loading MEAs are being tested in ongoing experiments and their results will be discussed and compared.

08 HYDROGEN↗
DOE OSTI2024

Macroscopic modeling of gas permeability in hierarchical micro/nanoporous media: A unified characterization of rarefaction using Klinkenberg theory and equivalent diameter

Estimating gas transport through a hierarchical micro/nanoporous system is challenging due to non-equilibrium gas dynamics. The primary difficulty lies in determining the rarefaction level, because identifying a representative flow dimension in a complex porous system with multiple pore scales is not straightforward. Our study performed a pore-level analysis for gas permeability in dual-scale porous media with varying porosity, throat size, and secondary pore size under different rarefaction conditions. We found that secondary porosity negatively affects permeability due to increased friction forces, with this influence growing as the secondary pore size and porosity increase until the secondary pore becomes comparable to the throat. However, rarefaction reduces the effects of secondary pores due to boundary slip. Traditional Knudsen number (Kn) calculations based on Darcy-defined height failed to accurately describe the rarefaction effects on gas permeability. Instead, we introduced an equivalent diameter to calculate the Kn, which provided an accurate normalization of apparent gas permeability independent of pore geometry. Furthermore, the extended Kozeny–Carman–Klinkenberg model developed in our previous study successfully yielded a macroscopic model for apparent gas permeability in hierarchical micro/nanoporous systems as a function of the traditional Darcy height and porosity.

04 OIL SHALES AND TAR SANDS↗