Predicting PEMFC performance from a volumetric image of catalyst layer structure using pore network modeling
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Sadeghi, Mohammad Amin↗
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Using Direct Numerical Simulation of Pore-Level Events to Improve Pore-Network Models for Prediction of Residual Trapping of CO2
Direct numerical simulation and pore-network modeling are common approaches to study the physics of two-phase flow through natural rocks. For assessment of the long-term performance of geological sequestration of CO 2 , it is important to model the full drainage-imbibition cycle to provide an accurate estimate of the trapped CO 2 . While direct numerical simulation using pore geometry from micro-CT rock images accurately models two-phase flow physics, it is computationally prohibitive for large rock volumes. On the other hand, pore-network modeling on networks extracted from micro-CT rock images is computationally efficient but utilizes simplified physics in idealized geometric pore elements. This study uses the lattice-Boltzmann method for direct numerical simulation of CO 2 -brine flow in idealized pore elements to develop a new set of pore-level flow models for the pore-body filling and snap-off events in pore-network modeling of imbibition. Lattice-Boltzmann simulations are conducted on typical idealized pore-network configurations, and the interface evolution and local capillary pressure are evaluated to develop modified equations of local threshold capillary pressure of pore elements as a function of shape factor and other geometrical parameters. The modified equations are then incorporated into a quasi-static pore-network flow solver. The modified model is applied on extracted pore-network of sandstone samples, and saturation of residual trapped CO 2 is computed for a drainage-imbibition cycle. The modified model yields different statistics of pore-level events compared with the original model; in particular, the occurrence of snap-off in pore-throats is reduced resulting in a more frontal displacement pattern along the main injection direction. Compared to the original model, the modified model is in closer agreement with the residual trapped CO 2 obtained from core flow experiments and direct numerical simulation.
Kohanpur, Amir H.↗
Fluid – Fluid Interfacial Area and Its Impact on Relative Permeability - A Pore Network Modeling Study
Abstract Relative permeability (kr) is commonly modeled as an empirical function of phase saturation. Although current empirical models can provide a good match of one or two measured relative permeabilities using saturation alone, they are unable to predict relative permeabilities well when there is hysteresis or when physical properties such as wettability change. Further, current models often result in relative permeability discontinuities that can cause convergence and accuracy problems in simulation. To overcome these problems, recent research has modeled relative permeability as a state function of both saturation (S) and phase connectivity (X). Pore network modeling (PNM) data, however, shows small differences in relative permeability for the same S-X value when approached from a different flow direction. This paper examines the impact of one additional Minkowski parameter (Mecke and Arns, 2005), the fluid-fluid interfacial area, on relative permeability to identify if that satisfactorily explains this discrepancy. We calculate the total fluid-fluid interfacial areas (IA) during two-phase (oil/water) flow in porous media using pore network modeling. The area is calculated from PNM simulations using the areas associated with corners and throats in pore elements of different shapes. The pore network is modeled after a Bentheimer sandstone, using square, triangular, and circular pore shapes. Simulations were conducted for numerous primary drainage and imbibition cycles at a constant contact angle of 0° for the wetting phase. Simultaneous measurements of capillary pressure, relative permeability, saturation, and phase connectivity are made for each displacement. Fluid-fluid interfacial area is calculated from the PNM capillary pressure, the fluid location in the pore elements, and the pore element dimensional data. The results show that differences in the relative permeability at the same (S,X) point is explained well by differences in the fluid-fluid interfacial area (IA). That is, for a larger change in IA at these intersection points, the permeability difference is greater. That difference in relative permeability approaches zero as the difference in IA approaches zero. This confirms that relative permeability can be modeled better as a unique function of S, X, and IA. The results also show that an increase in IA restricts flow decreasing the nonwetting (oil) phase permeability. This decrease is caused by an increase in the throat area fraction compared to the corner area as the total area IA increases. The wetting phase relative permeability, however, shows the inverse trend, in that its relative permeability is greater when IA becomes larger owing to a greater fraction of the total area associated with the corners. The area IA, however, impacts the nonwetting phase relative permeability more than the wetting phase relative permeability. Corner flow improves the wetting phase relative permeability because the wetting phase is continuous there. Finally, a sensitivity analysis shows that relative permeability a is more sensitive to change in S than they are for IA for the case studied implying that if only two parameters are used to model relative permeability it is better to choose S and X.
Engineering↗
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↗
4D structural changes and pore network model of biomass during pyrolysis
Biochar is an engineered carbon-rich substance used for soil improvement, environmental management, and other diverse applications. To date, the understanding of how biomass affects biochar microstructure has been limited due to the complexity of analysis involved in tracing the changes in the physical structure of biomass as it undergoes thermochemical conversion. In this study, we used synchrotron x-ray micro-tomography to visualize changes in the internal structure of biochar from diverse feedstock (miscanthus straw pellets, wheat straw pellets, oilseed rape straw pellets, and rice husk) during pyrolysis by collecting a sequence of 3D scans at 50 °C intervals during progressive heating from 50 °C to 800 °C. The results show a strong dependence of biochar porosity on feedstock as well as pyrolysis temperature, with observed porosity in the range of 7.41–60.56%. Our results show that the porosity, total surface area, pore volume, and equivalent diameter of the largest pore increases with increasing pyrolysis temperature up to about 550 °C. The most dramatic development of pore structure occurred in the temperature range of 350–450 °C. This understanding is pivotal for optimizing biochar’s properties for specific applications in soil improvement, environmental management, and beyond. By elucidating the nuanced variations in biochar’s physical characteristics across different production temperatures and feedstocks, this research advances the practical application of biochar, offering significant benefits in agricultural, environmental, and engineering contexts.
54 ENVIRONMENTAL SCIENCES↗
Towards replacing physical testing of granular materials with a Topology-based Model
In the study of packed granular materials, the performance of a sample (e.g., the detonation of a high-energy explosive) often correlates to measurements of a fluid flowing through it. The “effective surface area,” the surface area accessible to the airflow, is typically measured using a permeametry apparatus that relates the flow conductance to the permeable surface area via the Carman-Kozeny equation. This equation allows calculating the flow rate of a fluid flowing through the granules packed in the sample for a given pressure drop. However, Carman-Kozeny makes inherent assumptions about tunnel shapes and flow paths that may not accurately hold in situations where the particles possess a wide distribution in shapes, sizes, and aspect ratios, as is true with many powdered systems of technological and commercial interest. To address this challenge, we replicate these measurements virtually on micro-CT images of the powdered material, introducing a new Pore Network Model based on the skeleton of the Morse-Smale complex. Pores are identified as basins of the complex, their incidence encodes adjacency, and the conductivity of the capillary between them is computed from the cross-section at their interface. We build and solve a resistive network to compute an approximate laminar fluid flow through the pore structure. Here, we provide two means of estimating flow-permeable surface area: (i) by direct computation of conductivity, and (ii) by identifying dead-ends in the flow coupled with isosurface extraction and the application of the Carman-Kozeny equation, with the aim of establishing consistency over a range of particle shapes, sizes, porosity levels, and void distribution patterns.
36 MATERIALS SCIENCE↗
Three-Dimensional Pore Networks in Miocene Stevens Sandstone of California: Implications for CO 2 Geologic Storage
The Miocene Stevens Sandstone in the San Joaquin Basin of California is increasingly recognized as a promising candidate for CO 2 geological storage due to the enormous storage capacity, proven sealing, and existing infrastructure. In this study, computed microtomography imaging and pore network modeling were employed to investigate the influence of pore geometry and wettability on the CO 2 injectivity and residual trapping. Image analysis revealed that a significant fraction of the cement and matrix consists of microporous regions. The microporosity can substantially increase the overall pore space, yet its contribution to permeability remains modest, particularly in samples with low permeability. The intrinsic heterogeneity of turbidite reservoirs further complicates the reservoir properties among different layers. Two-phase flow simulations under varying wettability conditions (water-wet, weak water-wet, and neutral-wet) demonstrated that the CO 2 injection is predominantly controlled by macropores. CO 2 invades microporous regions only after these larger pores are filled. The presence of microporosity leads to a decrease in both initial and residual CO 2 saturations, with the magnitude of the reduction being influenced by wettability. Neutral-wet scenarios exhibit higher CO 2 mobility and thus lower residual trapping than water-wet scenarios. The results imply that heterogeneity in pore geometry and cement distribution across different layers can result in stratified CO 2 flow pathways, complicating efforts to predict injection performance. Overall, the Stevens Sandstone shows considerable promise for CO 2 geologic storage, but effective implementation will require detailed characterization of the pore structure as well as the integration of reactive fluid flow to account for potential mineral dissolution and fines migration.
fluids↗
Processing-Dependent Structure and Poroelasticity of Nafion in Liquid Water
Ionomers act as the solid polymer electrolyte membrane in many modern electrochemical devices, yet the role of their nanostructure in modulating the poroelastic response remains poorly understood, especially in liquid water, where few techniques can measure simultaneous transport-mechanical properties. Poroelastic Relaxation Indentation (PRI) is uniquely suited for measuring time-dependent transport-mechanical properties of porous solids, specifically hydraulic diffusivity, elastic modulus, Poisson’s ratio, and intrinsic permeability, for porous solids. While ionomers such as Nafion are not porous in the typical sense, Nafion has a nanophase-segregated structure that, when fully swollen in liquid water, behaves as a poroelastic solid with a coupled mechanical-transport response. Using a poroelastic framework, we investigate how casting and pretreatment of Nafion membranes alter their poroelastic response in liquid environments. We characterize both extruded and dispersion-cast Nafion membranes pretreated in water at 25 or 100 °C and relate the mechanical-transport properties to the ionomer structure via hydrophilic and intercrystalline domain spacing measured using Small-Angle X-ray Scattering (SAXS). At 25 °C, dispersion-cast membranes exhibit distinctly lower hydraulic diffusivity and intrinsic permeability than extruded membranes but with comparable mechanical properties. Pretreatment at 100 °C increases hydrophilic domain spacing, improving transport but at the expense of mechanical stiffness. Dispersion-cast membranes respond more strongly to pretreatment than extruded membranes. Using the Carman-Kozeny pore network model and the hydrophilic domain-spacing, we estimate the pore radius and tortuosity to show how pretreatment reduces structure-related tortuosity differences between dispersion-cast and extruded membranes. Here, in this work, we show that nanophase-segregated materials such as Nafion can be rigorously characterized using poroelasticity, resulting in physically meaningful transport-mechanical properties. Coupling PRI with SAXS provides insights into the nanostructural features that govern the coupled mechanical-transport response. By establishing PRI for a nanophase-segregated material, this approach opens avenues for this technique’s application in other hydrated polymeric materials not typically considered to be poroelastic.
Shen, Margaret [University of California, Berkeley↗
Stochastic generation of electrolyzer anode catalyst layers
Here, we introduce a stochastic methodology to reproduce the complex pore structure observed in commercial iridium catalyst layers. This method preserves the α pore (pores smaller than 250 nm) and β pore (pores greater than or equal to 250 nm) regions of the catalyst layer. The morphology of the generated materials was validated by comparing the pore size distributions of generated materials against those obtained from commercial materials imaged using x-ray nano computed tomography. We further demonstrate that the pore size distributions of the generated materials are statistically indistinguishable from the imaged catalyst layers, indicating that the stochastic methodology is capable of accurately reproducing catalyst layer morphology. Pore network modelling was conducted on the generated catalyst materials to simulate single-phase permeability, electrical conductivity, and ionic conductivity, and these properties were found to be within experimentally measured ranges for electrolyzer catalyst layers. Additionally, simulations were performed on the generated materials with varying ionomer and iridium catalyst loadings. As the ionomer loading is added, proton conductivity increases exponentially, which demonstrates the importance of optimizing ionomer loading, considering that these effects will be exacerbated in the hydration and temperature conditions of operating electrolyzers. The stochastic material generation method presented in this work is a powerful tool for the development of novel low loading catalyst layers, where the effect of various structural parameters on electrolyzer performance characteristics can be explored.
36 MATERIALS SCIENCE↗
Quantifying Dissolution Dynamics in Porous Media Using a Spatial Flow Focusing Profile
Abstract The diverse range of patterns in porous media formed by dissolution processes depends on the relative magnitude of flow, transport, and chemical reactions at pore surfaces. However, distinguishing between regimes often relies solely on qualitative, visual comparisons of emergent structures. Here, we propose a quantitative measure capable of identifying different regimes using the concept of the spatial flow focusing profile, which segments the medium into cross sections along the flow direction to calculate the flow focusing index for each section. We employ this measure in numerical simulations of a dissolving porous medium using a pore network model. We obtain a morphological phase diagram of dissolution patterns, which we characterize using the flow focusing profile. In particular, we demonstrate that analyzing the temporal changes in the profile allows one to quantitatively distinguish between wormholing and channeling. The transition between them is shown to be affected by the heterogeneity of the system.
58 GEOSCIENCES↗
Pore-Scale Transport Effects in Electrochemical CO 2 Reduction on Gold via Coupled Microkinetic-Transport Modeling
A pore-resolved modeling framework is developed to quantify how pore-scale transport affects the intrinsic microkinetics of CO 2 -to-CO on Au. A DFT-informed microkinetic model is coupled self-consistently to a Generalized-Modified Poisson–Nernst–Planck (GMPNP) transport description in a single, electrolyte-filled cylindrical pore, allowing local concentrations and potential to feed back into site-specific reaction rates. FIB-SEM is used to determine pore sizes within realistic electrode materials. Across pore diameters, d p = 10–6000 nm, the surface-averaged CO 2 reduction rate is systematically reduced relative to the ideal microkinetic baseline where mass transport is not accounted for; the effectiveness factor 𝜂 𝑠,CO 2 , which quantifies this ratio, decreases rapidly at more negative potentials and is about 1% near −1.0 V vs SHE due to reactant depletion. Spatial maps reveal pore-bulk alkalization that emerges at higher cathodic bias, with a small, near-wall pH dip due to electrostatic repulsion of hydroxide at the cathode interface. For a fixed aspect ratio L p /d p , narrower pores exhibit larger 𝜂 𝑠,CO 2 by shortening diffusion paths, whereas variations in the aspect ratio L p /d p play a secondary role. A dimensionless analysis (surface/bulk Damköhler numbers) delineates operating regimes. In conclusion, this work offers a concept for incorporating microkinetic models into homogenized porous-electrode models through effectiveness factors and pore-size distribution.
Au-catalyst↗
Striving to translate shale physics across ten orders of magnitude: What have we learned?
Shales will play an important role in the successful transition of energy from fossil-based resources to renewables in the coming decades. Aside from being a significant source of low-carbon intensity fuels, like natural gas, they also serve as geologic seals of subsurface formations that may be used to isolate nuclear waste, sequester CO 2 , or store intermittent energy (e.g., solar hydrogen). Despite their importance, shales pose significant engineering and environmental challenges due to their nanoporous structure and extreme heterogeneity that spans at least ~10 orders of magnitude in spatial scale. Two challenges inhibit a system-level understanding: (1) the physics of fluid flow and phase behavior in shales are poorly understood due to the dominant molecular interactions between minerals and fluids under confinement, and (2) the apparent lack of scale separation that prevents a reliable (closed) description of the physics at any single scale of observation. In this review, we focus on the latter issue and discuss scale translation, which in its broadest sense is transforming data or simulations from one spatiotemporal scale to another. While effective scale translation is not exclusive to shales, but all geologic porous media, the need for it is especially acute in shales given their high degree of heterogeneity. Classical theories like homogenization, while indispensable, fail when scales are not separated. Other methods, like numerical upscaling, scale-translate in only one direction: small to large, but not the reverse, called downscaling. However, the confluence of advances in three areas are bringing challenging problems such as shales within reach: increased computational power and scalable algorithms; high-resolution imaging and multi-modal data acquisition; and machine learning to process massive amounts of data. While these advances equip geoscientists with a wide array of experimental and computational tools, no individual tool can probe the entire gamut of heterogeneity in shales. Their effective use, therefore, requires an ability to bridge between various data types obtained at different scales. The aim of this review is to present a coherent account of computational and experimental methods that may be used to achieve just that, i.e., to perform scale translation. We provide a broader definition of scale translation, one that transcends classical homogenization and upscaling methods, but is consistent with them and accommodates notions like downscaling and data translation. After a brief introduction to homogenization, we review hybrid methods, numerical upscaling and its recent extensions, multiscale computing, high-resolution imaging, and machine learning. We place particular emphasis on multiscale computing and propose an algorithmic framework to bridge between the pore (micro) and Darcy (macro) scales. Throughout the paper, we draw comparisons between the various methods and highlight their (often hidden) similarities, differences, benefits, and pitfalls. We finally conclude with two case studies on shales that exemplify some of the methods presented.
58 GEOSCIENCES↗
Experimental Characterization of Hydrogen Diffusion in Shale Rocks for Geologic Storage Applications
As global energy systems undergo a transition to cleaner alternatives, geologic hydrogen storage has emerged as a promising solution for large-scale energy storage. A critical factor in determining the feasibility of this approach is the effectiveness of caprock formations, such as shale, in preventing hydrogen migration. This study investigates the diffusion behavior of hydrogen through shale to assess its suitability as a caprock for geologic hydrogen storage. Using a novel double-seal core holder design and a through-diffusion apparatus, hydrogen diffusion was measured through shale rock from the Eagle Ford and Wolfcamp Formations under dry conditions. These measurements were complemented by microstructural and mineralogical analyses using low-pressure nitrogen adsorption and X-ray diffraction. The effective diffusion coefficient of hydrogen in these shale caprocks ranged from 2.51 × 10 –8 to 9.85 × 10 –8 m 2 /s. Notably, we observed that the diffusion behavior was more related to the pore network structure and could not be attributed to differences in the total pore volume between shale types alone. Here, to further understand the role of pore network complexity, a fractal pore model was developed to correlate tortuosity with the fractal dimension of the pore structure (a measure of pore network complexity). The proposed model closely matched tortuosity values obtained from diffusion experiments, outperforming existing theoretical tortuosity–porosity correlations. These findings provide key quantitative parameters needed to assess the feasibility of geologic hydrogen storage as well as insights that can be applied to hydrogen storage in a range of geologic formations.
08 HYDROGEN↗
Soil porous microstructure control over soil organic matter mobility: A multimethod workflow for understanding chemistry-dependent organic matter binding in soil
Soil organic matter (SOM) has attracted a great deal of interest; particularly for its potential to mitigate human derived CO 2 emissions. Studies have demonstrated that SOM plays a critical role in carbon storage and CO 2 sequestration. However, the sorption properties of SOM, which influence its transport in pore water and stabilization within the soil, remain poorly understood. This study develops a workflow to: (1) examine compound-specific advective and diffusive transport and desorption behaviors, (2) quantify desorption rates through stop-flow and continuous-flow column experiments, and (3) evaluate the impact of soil microporosity on SOM mobility using high-resolution imaging and extractions. Intact core column experiments were conducted on Uncultivated (Natural) and Cultivated soil samples, both were arid soils, collected in Washington State. X-ray computed tomography was employed to measure porosity and pore connectivity, while Fourier-transform ion cyclotron resonance mass spectrometry was used to analyze SOM composition. The findings revealed that cultivation increased total carbon and nitrogen levels due to irrigation and fertilization, enhancing carbon capture potential in arid soils. In contrast, the Natural soil, characterized by higher porosity and connectivity, contained more oxidized carbon. Pore network analysis indicated that soil compaction in the Cultivated soil may lead to longer diffusion pathways, significantly influencing SOM transport and stability.
Hydraulic Properties↗
Pore-Scale Simulation of Spectral Induced Polarization
A new model was developed to simulate spectral induced polarization (SIP) in porous media. The model is based on a pore-network approximation of the soil or rock, in which bonds between pores are represented by equivalent circuits. In the circuit model, electrolytic and surface conduction occur in parallel, with the electrolyte behaving as a single resistor, and the mineral surface behaving as a resistor and capacitor in series. Based on the pore geometry, fluid conductivity, and mineral surface conductivity, an impedance network is generated. SIP spectra are calculated by solving the sinusoidal steady-state electrical problem for a range of frequencies. The new model provides a tool to bridge the gap between (1) our fundamental understanding of polarization processes at the scale of a single pore or grains and (2) existing simulation capabilities for macroscale systems that do not account for pore-scale properties. The model is implemented in Matlab and can solve two-dimensional and three-dimensional (2D and 3D) networks. Examples for regular cubic lattices are presented, but the method and code are flexible with respect to pore geometries and allow for future leveraging of existing open-source capabilities for generation of pore networks and extraction of network geometries from micro imaging of core samples.
58 GEOSCIENCES↗
Flow Reduction in Pore Networks of Packed Silica Nanoparticles: Insights from Mesoscopic Fluid Models
A modified many-body dissipative particle dynamics (mDPD) model is rigorously calibrated to achieve realistic fluid–fluid/solid interphase properties and applied for mesoscale flow simulations to elucidate the transport mechanisms of heptane liquid and water, respectively, through pore networks formed by packed silica nanoparticles with a uniform diameter of 30 nm. Two million CPU core hours were used to complete the simulation studies. Results show reduction of permeability by 54–64% in heptane flow and by 88–91% in water flow, respectively, compared to the Kozeny–Carman equation. In these nanopores, a large portion of the fluids are in the near-wall regions and thus not mobile due to the confinement effect, resulting in reduced hydraulic conductivity. Moreover, intense oscillations in the calculated flow velocities also indicate the confinement effect that contests the external driven force to flow. Here, the generic form of Darcy’s law is considered valid for flow through homogeneous nanopore networks, while permeability depends collectively on pore size and surface wettability. This fluid-permeability dependency is unique to flow in nanopores. In addition, potential dependence of permeability on pore connectivity is observed when the porosity remains the same in different core specimens.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Assessing pore network heterogeneity across multiple scales to inform CO2 injection models
Geologic heterogeneity is a key feature that must be considered when translations of scaled data are performed. This paper presents the assessment of geologic heterogeneity using a multiscale workflow that includes image analysis-based methods coupled with well log analysis to provide data in which fractals and machine learning methods estimate the carbon dioxide (CO 2 ) storage resource potential of a reservoir. The heterogeneity of rock properties of the complex Bell Creek reservoir in Montana, USA, was explored at the pore scale (~nm to mm), core scale (~mm to m), and well scale (~cm to m). The data used in this study included advanced image analysis of micro-CT (computed tomography) images (pore scale), thin sections (pore scale), plugs and core images (core scale) and well logs (well scale). The micro-CT images were segmented using a U-net segmentation approach into objects of pores and grains. Further, the segmented images were reconstructed into subvolumes of different sizes. Physical properties (porosity and permeability) and fractal dimensions were calculated for the various subvolumes, and Lorenz coefficient (Lc) values, a single parameter to describe the degree of heterogeneity within a pay zone section, were calculated from thin-section images and well logs. Porosity and fractal dimension values were used to estimate the 188-µm threshold of representative elementary volume (REV) in this study. Both the Lc and fractal dimension values were found to be negatively correlated. When these two parameters are combined, it is possible to discern differences in the complex porous networks of the samples analyzed in this study.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗