A Comparative Study of Pore Size Distribution in Gas Shales

Petrophysical characterization of unconventional rocks is an important challenge faced by the industry for reservoir evaluation. In particular, characterizing the pore size distribution (PSD) of tight rocks is challenging due to their small pore size and presence of clay minerals. In this paper, we develope a model to characterize PSD of shales using water adsorption isotherms. We apply the model on several shale samples and compare the results with the PSDs obtained from BET (Brunauer-Emmett-Teller) analysis using the N2 and CO2 adsorption isotherms. The proposed model describes the relationship between the cumulative adsorbed water and the size of the invaded pores due to capillary condensation during the water adsorption process. A set-up is designed to obtain water adsorption isotherms. The shale samples are placed in a sealed environment with a controlled relative humidity (RH). Different saturated salt solutions are used to control RH. At the end of the adsorption process, the model is applied to calculate PSD of the shale samples using their water adsorption isotherm. In order to evaluate the model results, we used BET analysis to obtain PSD from the N2 and CO2 adsorption isotherms. Moreover, the specific surface area (SSA), pore volume (PV) and the average pore size of the shale samples are also obtained from the BET analysis to compare the proposed model and BET results. The results of both BET and the proposed model indicate that the majority of the pores are smaller than 10 nm. However, the model results from the water adsorption show a bimodal PSD, while the BET analysis shows a unimodal PSD. Also, the model calculates small pores of less than 1 nm, while BET does not detect these pores. Water adsorption by clay minerals at low RH values is a possible reason for this discrepancy. Furthermore, the sample with higher clay content shows larger hysteresis at the end of the sorption (adsorption-desorption) experiment; suggesting that the clay-bound water cannot be easily removed during the desorption process.

The microporous-mesoporous structure of nanoporous carbon and modified carbon electrodes has a strong influence on the electrochemical characteristics of the devices like supercapacitors, polymer electrolyte fuel cells and electrolysers, gas storage devices, as well as of Li-ion and Na-ion batteries. For that reason, it is crucial to have a good understanding of the porosity and hierarchical structure of carbon and modified carbon materials used [1]. As a standard method, the nitrogen adsorption measurements and various analysis theories are used. These models need the pore shape as an input parameter for detailed calculations, however, often the slit-shaped pore model is postulated without additional verification [1]. This assumption is also very often transferred to the behaviour of carbon based materials in different applications leading to some serious misinterpretations. For cost-effective hydrogen and methane based economy, efficient methods for hydrogen and methane storage are urgently needed. To improve the gas storage properties, the fundamental understanding of the confinement of the gas in microporous-mesoporous materials is inevitable. In particular, the role of confinement dimensions in the mass transfer of the hydrogen, methane as well as oxygen molecules has huge impact on the fuel cell characteristics. Our research focuses on detailed estimation of pore shape and size in various carbide-derived carbons and other carbon materials using various standardized and novel methods, like nitrogen, hydrogen and carbon dioxide adsorption measurements. All carbon samples were dried under vacuum at 350 оC at least for 24 h prior to each measurement. N2 sorption analysis at -196 оC and CO2 sorption analysis at 0 оC were carried out on an ASAP 2020 instrument (Micromeritics, USA). The experimental data were treated with classical models (BET and t-plot) as well as different NLDFT models available through 3Flex and SAIEUS (Micromeritics, USA) software [2,3]. The results for pore size distribution (PSD) calculations from N2 isotherms using a slit shape pore model and model “Carbon-N2, 2D-NLDFT Heterogeneous Surface” [4,5] (demo software SAIEUS, Micromeritics, USA) will be reported. The pore size distribution data calculated from CO2 sorption isotherms using a slit shaped pore model and model “CO2-DFT Model” (software 3Flex, Micromeritics, USA) will be discussed. Although, the pore size distributions calculated from CO2 have high level of roughness and several model artefacts (e.g. around 0.7 nm) [6,7], the results generally support the findings from N2 sorption isotherms. Raman spectra analysis, small-angle neutrons scattering and small angle X-ray scattering combined with the FIB-SEM and high resolution TEM data have been used. The results obtained are compared to the behaviour of these materials in different energy storage/conversion related devices like supercapacitors [8,9] and polymer electrolyte fuel cells 10]. As a result, the importance of hierarchical porous structure and pore shape along with pore size (pore size distribution) of used carbon materials in the energy technology applications will be addressed and demonstrated. The hydrogen sorption parameters will be compared with the methane sorption characteristics as well as correlated with PEM fuel cell and supercapacitor characteristics. Acknowledgments Authors would like to thank HZB and PSI for the allocation of neutron radiation beamtime on instruments V16 and FOCUS, respectively. The Estonian Ministry of Education and Research (institutional research project IUT20-13, personal research grant PUT55) and European Regional Development Fund (The Centres of Excellence TK117 and, TK141) for financial support.

The microporous-mesoporous hierarchical structure of nanostructural carbon and modified carbon materials has a strong influence on the electrochemical characteristics of the electrical energy conversion and storage devices [1-4]. To improve the mass transfer rate, the understanding of the accumulation mechanisms of the ions in microporous-mesoporous materials is inevitable having huge impact on the power and energy density characteristics of supercapacitors, Li- and Na-ion batteries as well as fuel cells. Therefore, it is crucial to have a good understanding of the graphitization level, porosity and hierarchical structure of carbon and modified carbon materials used [1-5]. Therefore, systematical analysis of the gas adsorption, Raman, X-ray diffraction, scanning electron microscopy, photoelectron spectroscopy (including synchrotron beam based method), high-resolution transmission electron microscopy (with EELS and SAED) and small-angle neutron scattering data for various carbon materials prepared by high-temperature chlorination, hydrothermal carbonization, etc. methods will be given. Comparison with small-angle X-ray scattering data [6] will be given. The data obtained by gas-phase analysis methods will be compared with cyclic voltammetry, constant current charge/discharge, electrochemical impedance and constant power discharge data. Influence of electrolyte chemical composition, solvent characteristics (aqueous and non-aqueous) and ionic liquids with and without non-aqueous solvent additions will be discussed in combination with hierarchical porosity, graphitization level and particle size analysis data. All carbon samples were very carefully reduced with hydrogen at 800 оC, thereafter dried under vacuum at 350 оC at least for 24 h priori each measurement. N2 sorption analysis at -196 оC, Ar at -186 oC and CO2 sorption analysis at 0 оC were carried out on an ASAP 2020 instrument (Micromeritics, USA). The experimental data were treated with classical models (BET and t-plot) as well as different NLDFT models available through 3Flex and SAIEUS (Micromeritics, USA) software [7,8]. The results for pore size distribution (PSD) calculations from N2 isotherms using a slit shape pore model and model “Carbon-N2, 2D-NLDFT Heterogeneous Surface” [9,10] (SAIEUS, Micromeritics, USA) will be reported. The pore size distribution data calculated from CO2 sorption isotherms using a slit shaped pore model and model “CO2-DFT Model” (software 3Flex, Micromeritics, USA) will be discussed. Although, the pore size distributions calculated from CO2 have high level of roughness and several model artefacts (e.g. around 0.7 nm) [11,12], the results generally support the findings from N2 sorption isotherms. In addition, Raman spectra analysis, small-angle neutrons scattering and small angle X-ray scattering combined with the FIB-SEM and HR-TEM data will be discussed. The results obtained will be compared to the behavior of these materials in different energy storage/conversion related devices like supercapacitors [1-6] and Li- and Na-ion battery negatively charged electrodes [4]. Thus, the importance of graphitization level, hierarchical porous structure and pore shape along with pore size distribution data for carbon materials energy and power densities will be addressed and demonstrated. Acknowledgments Authors would like to thank HZB and PSI for the allocation of neutron radiation beamtime on instruments V16 and FOCUS, respectively; and The Estonian Ministry of Education and Research (institutional research project IUT20-13, personal research grant PUT55) and European Regional Development Fund (The Centres of Excellence 3.2.0101–0030 and 2014-2020.4.01.15-0011) for financial support.

summaryExperimental investigations indicated that over wet periods the moisture content of dead attached ash twigs was very variable. Frequently they were subject to very rapid and large changes in moisture content, of the order of ± 40% in 24 h. Over wet periods drying of twigs was apparently due mainly to drainage, the rate of which was determined by a number of interrelated factors including density, diameter and degree of bark loss. Over dry periods the moisture content of twigs was less variable and drying was due mainly to evaporation. Water sorption isotherms were determined for twigs and the form of these isotherms was essentially similar to that recorded for sapwood of various trees by other authors. The form of the sorption isotherm was affected by density, a factor related to their state of decay. The sorption isotherms indicated that the pore size distribution within twigs was markedly different from that in typical branch sapwoods. The isotherms were used to estimate water potential variation in dead attached twigs in the field.

Mesoporous silica SBA-15 was modified in a three-step process to obtain a material with poly-N-isopropylacrylamide (PNIPAAM) grafted onto the inner pore surface. Water sorption calorimetry was implemented to characterize the materials obtained after each step regarding the porosity and surface properties. The modification process was carried out by (i) increasing the number of surface silanol groups, (ii) grafting 1-(trichlorosilyl)-2-(m-/p-(chloromethylphenyl) ethane, acting as an anchor for (iii) the polymerization of N-isopropylacrylamide. Water sorption isotherms and the enthalpy of hydration are presented. Pore size distributions were calculated on the basis of the water sorption isotherms by applying the BJH model. Complementary measurements with nitrogen sorption and small-angle X-ray diffraction are presented. The increase in the number of surface silanol groups occurs mainly in the intrawall pores, the anchor is mainly located in the intrawall pores, and the intrawall pore volume is absent after the surface grafting of PNIPAAM. Hence, PNIPAAM seals off the intrawall pores. Water sorption isotherms directly detect the presence of intrawall porosity. Pore size distributions can be calculated from the isotherms. Furthermore, the technique provides information regarding the hydration capability (i.e., wettability of different chemical surfaces) and thermodynamic information.

Water sorption isotherms of Kraft lignin and its composites

Porosity evolution in oil-prone source rocks

The measurement of the diffusion coefficient and the sorption isotherm of water in paint films

The enzymatic properties of Plumeria rubra latex have been evaluated for the first time, showing a high activity in both hydrolysis and synthesis reactions, and compared to the biocatalytic behavior of babaco (Vasconcellea x Heilbornii cv.) latex. Both biocatalysts have been optimized by studying the various parameters that influence reaction kinetics. The optimum temperatures for hydrolysis reactions were 50 and 55 degrees C for babaco and Plumeria, respectively. The optimum pH for babaco latex was 7, whereas for Plumeria latex, two optimal pH values (4 and 7) were observed. With regard to esterification and acyl transfer reactions such as alcoholysis and interesterification, the influence of thermodynamic water activity on reaction yields was determined and correlated with water sorption and desorption isotherms. When babaco latex is used as a biocatalyst, optimal synthesis reaction yields are obtained when the enzymatic extract is stabilized at a water activity value of 0.38, which corresponds to a water content of 5.7%. This optimal level of hydration is located on the linear portion of the biocatalyst's sorption isotherm, where the water molecules exhibit high-energy interactions with the protein network. In synthesis reactions (esterification, alcoholysis, and interesterification) biocatalyzed by Plumeria latex, correlation between best reaction yields and water activity cannot be done. Indeed, the sorption isotherm plot has an atypical shape, indicating that water might be trapped in the latex matrix and, consequently, that the water content of the biocatalyst is highly dependent on the hydration history of the latex.

Air drying kinetics at 35, 50, 60 and 75 °C and water adsorption and desorption isotherms at 5, 25, 40 and 55 °C of the brown seaweed Bifurcaria bifurcata were obtained. Water sorption isotherms were modelled by means of the two-parameter Halsey model. A model to estimate equilibrium moisture content of adsorption and desorption processes as function of water activity and temperature simultaneously was obtained by means of linear correlations of Halsey model parameters with temperature. Water sorption isotherms were analysed by a thermodynamic approach to obtain properties such as net isosteric heat of sorption, net equilibrium heat, differential and integral entropy. Monolayer moisture content evaluated by BET model corresponded to the moisture content at which local minimum integral entropy value was observed for sorption processes. Air drying kinetics at different temperatures were modelled using the Page model. The two parameters of the Page model were linearly correlated with temperature. The goodness of the fits was evaluated by evaluation of the coefficients of determination and root mean square errors.

We analyze a compiled stack of Scanning Electron Microscopy (SEM) images of an Eagle Ford shale sample to assess pore structure and complex pore connectivity. In recent years, shale and tight oil formations have played an important role as energy resource. However, uncertainties associated with pore structure and pore connectivity as an important parameter controlling the well productivity remain to be resolved; that is why, high-resolution image processing has been an emerging research tool. In this study, 600 contiguous high-resolution SEM images of a 6 μm Eagle Ford sample is analyzed using an image processing software. We obtain 2D and 3D porosity and pore size distribution. In addition, we map out the connected pores to obtain the connected porosity from 3D volumetric fraction. Next, we analyze total and connected porosity as a function of sample size in both forward and backward sequences. Finally, results obtained from the shale sample is compared with a sandstone sample to determine differences in their pore structure properties. We conclude that the connected porosity is 6.1% for the shale sample, smaller than that of the sandstone (19.6%). The attributed pore size distribution ranges from 0.01μm to approximately 0.1μm, while the sandstone’s pore radius size ranges from 1 μm up to 12.7 mm. Through evaluation of sandstone sample, it turns out that 3D total porosity of the sandstone sample is almost the same as the connected porosity. Moreover, although the connected porosity of the stacked images gradually and slightly decreases as the sample size increases. However, for the shale sample, total porosity remains almost constant as a function of sample size while the connected porosity significantly decreases from 13.3% to 6.1%. More interestingly, if the images are analyzed in the backward sequences, then both porosity and the connected porosity increase. Overall, the results suggest that for the studied shale sample, Representative Elementary Volume (REV) describing pore connectivity is around 4 μm. The results from this study will provide a new insight into complex pore structure and help better understand the production performance of shale reservoirs. In addition, the outcome of this paper would have some implications on research work related to fluid flow in shale.

Summary: The origin of porosity and mechanisms of fluid flow at the presence of organic matter and clay minerals in source rocks is poorly understood. Burial and maturation of the source rock affects all types of pore systems in these fine-grained rocks. Kerogen decomposition and consequent shrinkage change the load bearing state of the minerals and organic matter. Porosity in the kerogen is generated since early stages of maturation but it is only preserved if the kerogen particles are sheltered in a supporting frame of load bearing minerals. Geologic evidence confirms that the expulsion process is not 100% efficient. The expulsion efficiency and its control factors are poorly constrained. Presence of clay minerals and the organic matter affect log responses by falsifying porosity and resistivity measurements. In order to understand porosity evolution and the interaction of byproducts and rock minerals during the course of maturation one must study source rock samples with different range of maturity. In this paper, we studied the evolution of porosity in self-sourcing mudrocks. We measured pore size distributions (PSD) and specific surface areas (SSD) in native state and after successive extraction of the source rocks with solvents of increasing polarities. The PSD and SSA measured after each washing show evolution of the pore system with successive cleaning. Most significant is the recovery of kerogen-hosted pores with removal of hydrocarbons. We found that kerogen-hosted pores were only recovered in the less clay rich samples. This observation confirms the significance of sheltering effect from load bearing minerals. These studies will help us to understand how the log responses must be interpreted at the presence of organic matter and clay minerals and develop practical workflows for integrating geochemical data with well logs for petrophysical characterization of self-sourcing systems.

Sorption and desorption isotherms of water at 27 °C have been determined for a series ofα-substituted nylons 3 (methyl to butyl and phenyl derivatives), which at room temperature are deep below the respective glass transition temperatures. It follows from the rate of establishment of sorption equilibria as well as from sudden changes of the sorption isotherms, that in all samples, without respect to their different structure, a change of the mechanism takes place when vapour activity passes through a value of about 0.25. From the point of view of the amount of water (C1) sorbed on the accessible amide group with water activity equal 1 (accessibility having been determined by means of deuteriation), the methyl, dimethyl and phenyl derivative sorb like non-substituted nylons 2 to 6 (C1=3/2), the other samples with longer aliphatic substituents sorb like nylon 8 and higher nylons (C1=1/2).

Water sorption calorimetry has been used for characterization of 2D hexagonally ordered mesoporous silica SBA-15. Experimental data on water sorption isotherm, the enthalpy, and the entropy of hydration of SBA-15 are presented. The results were compared with previously published results on MCM-41 obtained using the same technique. The water sorption isotherm of SBA-15 consists of four regimes, while the sorption isotherm of MCM-41 consists only of three. The extra regime in the water sorption isotherm for SBA-15 arises from filling of intrawall pores, that are present in SBA-15 but absent in MCM-41. The water sorption isotherms of the two types of mesoporous silica were analyzed using the Barrett-Joyner-Halenda approach. For the BJH analysis, t-curves of silica with different degrees of hydroxylation were proposed. Comparison of water and nitrogen t-curves shows that, independent of hydroxylation of silica surface, the adsorbed film of water is much thinner than the adsorbed film of nitrogen at similar relative pressures. This fact decreases the uncertainty of the assessment of porosity with water sorption originated from variations in surface properties. The pore size distribution of SBA-15 calculated with BJH treatment of water sorption data is in good agreement with nitrogen NLDFT results on the same material.

Prediction of contaminant transport in concrete subjected to short cyclical wetting and drying processes is integrally bound to prediction of the moisture flux. The concrete is unsaturated and the non-linear contaminant and moisture fluxes are not described by simple constant diffusion methods. This thesis presents, and partially justifies, a thermodynamic model for prediction of moisture movement in concrete, at all moisture contents commonly encountered. The wetting process is examined with Nuclear Magnetic Resonance (NMR) images during a simple absorption (sorptivity) experiment. Diffusivity functions are derived via a novel analytical approach and a universal diffusivity is suggested. Water sorption and desorption isotherms are measured on large concrete samples. van Genuchten’s retention function is successfully used to model the results. The unrelia-bility of the water sorption method at high moisture contents is illustrated by comparison with Mercury Intrusion Porosimetry (MIP). The BJH method is exploited to provide a methodology for estimating the water sorption isotherm from MIP. Mualem’s conductivity model is assessed with the water retention and NMR results. This thorough validation of the model yields a tortuosity parameter that is different to that commonly assumed. An analytical relationship between the sorptivity and the saturated permeability suggests the experimental the long-term unsaturated permeability overesti-mates the unsaturated conductivity function, and as such should be used judiciously when predicting unsaturated flow processes. Mualem’s conductivity model is further exploited to provide unsaturated air and vapour functions that are experimentally justified. The thermodynamic description of water movement and the hydraulic functions that are developed in the thesis are incorporated into T r inCet , a transient heat and mass trans-fer model based on the Finite Element Method (FEM). The complex coupled behaviour of air, liquid, vapour and temperature are well handled under a variety of common cyclical boundary conditions. The thesis presents all necessary experimental results required for validation of a com-plex, but easily described, model for moisture movement. It covers disparate ground to provide a powerful numerical model of unsaturated moisture movement in concrete under short-term cyclical processes.