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Computer program calculates surface area and pore size distribution of powders, metals, ceramics, and catalysts, and prints and plots the desired data directly. Surface area calculations are based on the gas adsorption technique of Brunauer, Emmett, and Teller, and pore size distribution calculations are based on the gas adsorption technique of Pierce.
Accurate permeability estimation is essential across subsurface engineering applications but remains challenging due to the complex pore structures of natural geomaterials. Traditional empirical methods and simplified theoretical models often inadequately capture the role of pore size distribution and connectivity. Here, this study develops a statistical and simulation-informed permeability model that collapses pore-scale complexity into a compact scaling of the form k = αϕμ d 2 , where ϕ is porosity, μ d is mean pore size, and α is a weakly varying coefficient. By combining pore network simulations with statistical analysis of unimodal and bimodal pore size distributions, we identify three key findings: (i) permeability is much more sensitive to mean pore size than to porosity; (ii) across extensive datasets, the ratio σ d /μ d (standard deviation to mean) clusters around a characteristic value ∼0.4, allowing the effects of the full pore size distribution to be represented by μ d and a narrowly varying α ≈ 0.05; and (iii) for bimodal systems, there exists a critical fraction of small pores ∼0.78 above which flow becomes small-pore dominated, enabling the definition of an effective flow-controlling pore population and facilitating simplified permeability estimation for such systems. The resulting model, which requires only porosity and a representative mean pore size as inputs, is validated against comprehensive experimental datasets (>1700 samples) spanning diverse soils and rocks and achieves good predictive accuracy. Overall, this work provides a physically grounded yet practically simple permeability estimator suitable for subsurface engineering, environmental protection, and resource management applications.
This research established a systematic method to generate various pore-size distributions (PSDs) and studied the effect of PSDs on the shock compaction response of granular materials using two-dimensional mesoscale simulations under identical porosity. Simulations utilized various PSDs for three particle shapes (circle, ellipse, and square). Contacting particle configurations using three PSDs, characterized by spatially uniform distributed pores to heterogeneous distributed pores, and non-contacting particle configurations under a single case of PSD were tested. The PSD of generated particle sets was characterized using coordination number, mean diameter, and bimodality coefficient as statistical metrics. Mesoscale simulations showed that regardless of the conditions of pore distributions, shock compaction of granular materials consistently demonstrates a precursor, shock compaction front, and end. However, the shock compaction velocity of contacting particles was dependent on the PSDs despite the constant initial porosity. The compaction velocity was faster in particle configurations with relatively uniform pore distributions than in heterogeneous pore distributions, which our study demonstrated can be attributed to particle rearrangement during compaction. Circular-shaped particles had high sensitivity in shock compaction response to the various PSDs. Furthermore, a contacting particle configuration tended to propagate the shock compaction wave relatively faster than particles that were in a non-contact configuration. This study established the relative importance of considering PSD as a metric over the coordination number in studies of the shock compaction response of granular materials. Further, insights are provided on the evolving shock substructure to characterize the shock compaction response of granular materials.
Fortran 4 computer program for calculating and plotting surface area and pore size distribution data obtained by gas adsorption
The Pore2Chip Python package is designed to create 2D micromodels using extracted data from 3D X-ray computed tomography (XCT) images. This package helps analyze soil structure and function, allowing for the investigation of hydro-biogeochemical processes that impact mineral extraction and reactivity, oxygen concentrations, and nutrient availability in disturbed or managed soils. Key metrics encompass pore size distributions, pore throat size distributions, and connectivity (pore coordination numbers). The final output is a 2D scalable SVG design representing a core or aggregate. Designs can be fabricated with methods such as laser etching, 3D printing, and photolithography.
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Reducing Ir loadings in proton exchange membrane water electrolyzer anodes is critical for lowering capital expenses. Loading reduction could be achieved by improving the Ir activity via doping/alloying and/or the development of advanced microstructures. However, the anode porous transport layer (PTL) is a comparatively simple component whose properties also impact Ir utilization. Therefore, well-designed PTLs may also enable reduced Ir loadings. In this work, we survey eight PTLs from various manufacturers to observe their impact on cell performance at low (0.4 mg Ir cm -2 ) and ultralow (0.1 mg Ir cm -2 ) Ir loadings. The PTLs were characterized by their microstructural properties, including porosity, particle size distribution, and pore size distribution. Electrochemical cell performance was correlated to PTL morphology, and it was found that PTLs with lower porosities and smaller particle and pore radii enabled good performance even at ultralow Ir loadings. 1000-h durability testing indicated that using lower porosity PTLs can significantly improve durability behavior. A runaway voltage phenomenon was observed during durability testing of cells with ultralow Ir loadings, which was caused by increases in both anode and cathode overpotentials. Furthermore, we observed that the beginning of test performance of 0.1 mg Ir cm -2 cells correlates to the 1000-h degradation rates of 0.4 mg Ir cm -2 cells, suggesting that for the Ir catalyst used in this work, short-term testing at ultralow loadings can be used as an indicator of long-term degradation at higher loadings.
Characterizing the pore structures and transport properties of low-permeability shales is critical for evaluating these formations as potential seals or storage sites for geological CO 2 sequestration. Here, we use low-pressure gas adsorption in conjunction with nuclear magnetic resonance (NMR) to characterize the pore-size distribution of shales before and after injection of supercritical CO 2 . Nitrogen gas was used as the detecting phase for the adsorption experiments and pentane liquid was used for the NMR experiments. We also performed time-resolved NMR and gravimetric microbalance measurements to observe mass transport during desaturation. We use these data to estimate the self-diffusion coefficient of pentane and changes in the saturation state of the pore network. We analyzed samples with a range of compositions from the Wolfcamp shale before and after exposure to supercritical CO 2 for 3 days. Integrating the gas adsorption and NMR data shows how supercritical CO 2 injection alters the pore-size distribution for pore sizes <1 nm to 1 mm. Finally, our results provide insights on how the pore structure and mass transport properties of different shale lithologies may evolve during storage of supercritical CO 2 .
Compositions are provided for efficient uranium extraction, for example from wastewater, seawater, or other water sources. The compositions can include a functionalized porous organic polymer functionalized with one or more uranium binding moieties, e.g. having a plurality of amidoxime or amidrazone groups covalently attached thereto. The compositions can include covalent organic frameworks, porous aromatic frameworks, and various porous organic polymers, especially those having a hierarchical pore size distribution over a range of pore sizes. The compositions can have functional groups such as amidoxime or an amidrazone covalently attached thereto. The hierarchical pore size distribution can be determined based upon at least 60% of the pore sizes in the range of pore sizes having a pore volume of at least 0.01 cm 3 g −1 in the pore size distribution at 77 K. Methods of making the compositions and methods of using the compositions are also provided.
Statistical analysis and correlation between pore-size distribution and fracture strength distribution using the theory of extreme-value statistics is presented for a sintered silicon nitride. The pore-size distribution on a polished surface of this material was characterized, using an automatic optical image analyzer. The distribution measured on the two-dimensional plane surface was transformed to a population (volume) distribution, using the Schwartz-Saltykov diameter method. The population pore-size distribution and the distribution of the pore size at the fracture origin were correllated by extreme-value statistics. Fracture strength distribution was then predicted from the extreme-value pore-size distribution, usin a linear elastic fracture mechanics model of annular crack around pore and the fracture toughness of the ceramic. The predicted strength distribution was in good agreement with strength measurements in bending. In particular, the extreme-value statistics analysis explained the nonlinear trend in the linearized Weibull plot of measured strengths without postulating a lower-bound strength.
Pore structure study is an important part of unconventional shale reservoir characterization, since the pore system provides the primary petroleum storage space and fluid flow pathways. Previous studies have suggested that the pore structure is related to the total organic carbon (TOC) content, mineral compositions, and the maturity of the organic matter (OM). However, few studies have focused on the mineral grains, the primary grains being deposited but before cementation, which are the building blocks of shale. Eight Woodford Shale outcrop samples from southern Oklahoma were chosen to study the effects of mineral grain size on the pore structure characterization, using multiple and complementary experimental approaches, including laser diffraction, mineralogy, TOC, pyrolysis, liquid immersion porosimetry, mercury intrusion porosimetry, gas physisorption, (ultra) small angle X-ray scattering, scanning electron microscopy, and spontaneous imbibition. The results from different experiments of eight samples show that the Woodford Shale has the mean mineral grain diameters at 3–6 μm, a wide range of porosity at 3–40% and pore diameters at 50–1,000 nm, and various pore connectivity. Grain size variation was probably caused by the sea-level fluctuation during its deposition, which affect the porosity, pore size distribution, and pore connectivity. With decreasing mineral grain sizes, the porosity tends to increase while the pore connectivity worsens. The results also indicate that OM and carbonates in this low-maturity Woodford Shale could block the pores and decrease the porosity. Coupling with the grain size analyses, the control of depositional environment on grain sizes and subsequent effects on pore structure is identified. The pore structure characteristics over a wide pore-diameter range provided by multiple experiments could improve the understanding of storage space and fluid flow in the Woodford Shale to further increase its petroleum production.
This investigation provides both experimental and theoretical analyses of biomass char gasification kinetics over 1150–1350 °C in the environment of CO 2 , H 2 O and combinations of these reactants. The experimental data include continuous measurements of particle mass, external and internal temperatures, shape, and size with periodic but not continuous measurements of char porosity, pore size distribution, and pore surface area. The model describes heterogeneous char gasification for poplar wood, corn stover and switchgrass in different shapes and industrially relevant sizes (12.5 mm and smaller). Nonlinear least-squares regression produces optimized power-law model parameters for global kinetics that describe biomass char gasification with respect to both CO 2 and H 2 O separately and in combination. A single set of kinetic parameters describes reaction rates for all three fuels. Model simulations agree with measured data at all stages of char conversion even though the observed mass loss rates change significantly with conversion. In conclusion, the change in rate with conversion depends strongly on ash content, and this investigation provides a simple and theoretically based reaction rate expression that includes the effect of inert ash occupying an increasing portion of the reactive surface with increased conversion.
Conventional silica aerogel monoliths can provide remarkable thermal insulation but the presence of large pores (> 30 nm) tends to scatter visible light and render the material opaque or translucent instead of transparent. In addition, they are prone to cracking during synthesis and handling which makes them difficult to integrate in products and in particular in window solutions. This project developed two new solgel synthesis methods using silica precursors or preformed silica nanoparticles and ambient drying to produce mesoporous organo-silica monoliths. The monoliths were (i) thermally insulating, (ii) optically transparent, (iii) flexible, and (iv) hydrophobic. They feature porosity ranging from 50% to 90% with narrow pore size distribution with pore less than 20 nm resulting in excellent optical clarity (haze < 2%) and very low thermal conductivity (< 30 mW/mK). Interestingly, not only porosity but also pore size and mass fractal dimension were found to affect the thermal conductivity of the mesoporous silica. The superior transparency of the monoliths was shown to be attributed to dependent scattering among silica nanoparticles. Flexibility was achieved through trimethylchlorosilane surface modification. Furthermore, process scale-up and integration of the ambigel monoliths into window solutions using optically clear adhesives were also demonstrated in 6”x6” double-pane windows. The aerogel and the window solution were shown to be durable to accelerated aging under UV, moisture, and/or temperature gradient and thermal cycling. Overall, the window solution achieved the technical performance and the cost target of $10/sqft set for the SHIELD program. However, scaling to industry relevant scale (> 10’x10’) remains a challenge due to requirements on the drying process and fume hood size and to the propensity of large aerogel slab to crack during drying.
To maximize performance in starved, multiplate cells, the cell design should rely on techniques which widen the volume tolerance characteristics. These involve engineering capillary pressure differences between the components of an electrochemical cell and using these forces to promote redistribution of electrolyte to the desired optimum values. This can be implemented in practice by prescribing pore size distributions for porous back-up plates, reservoirs, and electrodes. In addition, electrolyte volume management can be controlled by incorporating different pore size distributions into the separator. In a nickel/hydrogen cell, the separator must contain pores similar in size to the small pores of both the nickel and hydrogen electrodes in order to maintain an optimum conductive path for the electrolyte. The pore size distributions of all components should overlap in such a way as to prevent drying of the separator and/or flooding of the hydrogen electrode.
Capacitive deionization (CDI) is a promising technology that has gained interest for the desalination of brackish water. Hierarchically porous carbons are commonly used as electrodes for CDI due to their high surface areas and controlled pore size distributions that maximize ion adsorption capacity and rate. Electrospinning is an effective way of generating carbon nanofibers with high inter-fiber macroporosity that can be further modified to improve surface area, total pore volume, and pore size distribution. This work describes the use of sacrificial mesopore formers in tandem with a micropore etching technique to induce hierarchical porosity in electrospun fibers. Mesopores are formed via the dissolution of silica nanoparticles that are introduced into the fibers during the electrospinning step. After mesopore formation, micropores are etched into the resulting surface through KOH impregnation and thermal activation. This sequential technique creates a hierarchical network of pores from the inherent macroporosity of the fiber network, to the mesopores, and finally micropores to simultaneously maximize surface area and accessibility. Micropore formation is optimized to maximize specific surface area while maintaining physical integrity of the fibers. Further, the combination of mesopores and micropores enables fast ion adsorption rates and capacity. Carbon fiber electrodes fabricated in this method achieve specific surface areas exceeding 1400 m 2 g -1 , with pore volumes exceeding 1.0cc g -1 . The pore size distributions are highly controlled, with 80% of total pore volume coming from pores <20nm in radius. In 500 ppm constant voltage CDI tests, these fiber electrodes obtain a salt adsorption capacity of over 14 mg g -1 at a salt adsorption rate of ~4mg g -1 min -1 , showcasing the high capacity matched with high rate of these easily fabricated, inexpensive materials.
It has been hypothesized that gravity has an effect on the formation and resulting microstructure of sol-gels. In order to more clearly resolve the effect of gravity, pores may be non-destructively analyzed in the wet gel, circumventing the shrinkage and coarsening associated with the drying procedure. We discuss the development of an electrophoretic technique, analogous to affinity chromatography, for the determination of pore size distribution and its application to silica gels. Specifically a monodisperse charged dye is monitored by an optical densitometer as it moves through the wet gel under the influence of an electric field. The transmittance data (output) represents the convolution of the dye concentration profile at the beginning of the run (input) with the pore size distribution (transfer function), i.e. linear systems theory applies. Because of the practical difficulty in producing a delta function input dye profile we prefer instead to use a step function. Average pore size is then related to the velocity of this dye front, while the pore size distribution is related to the spreading of the front. Preliminary results of this electrophoretic porosimetry and its application to ground and space-grown samples will be discussed.