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Kerogen has a lower affinity to hydrogen than methane; thus, it allows hydrogen to flow more easily, but it is unclear how the permeabilities of hydrogen and methane differ. This study determines the single-phase permeability of hydrogen and compares it with methane permeability in organic-rich caprock. It takes into account adsorption to the pore wall and slippage at the boundary. It implements the two processes at 370 K for pressures from 500 to 4000 psi to obtain the hydraulic conductance of a sub-100-nm conduit. It then relates them to the macroscopic behavior via network modeling. Lower pressures represent depleted gas reservoirs in the subsurface. Decreasing pore pressure enhances hydrogen transport by reducing its adsorption to the pore wall and transitioning its behavior from continuum to discrete particles, leading to first- or second-order slippage. The results show that hydrogen conductance, q i n − s i t u (H 2), is always larger than the reference conductance without adsorption and slippage (q 0). Hydrogen permeability, k i n − s i t u (H 2), is also larger than methane permeability, k i n − s i t u (CH 4), while the permeability values differ by 70% − 130%, depending on the pore pressure. This study also determines the conduit size corresponding to the ratio of hydrogen permeability to methane permeability at in-situ conditions by comparing it with the ratio of hydraulic conductance of hydrogen to methane. The results have applications in underground hydrogen storage by indicating how hydrogen flow changes with pressure in ultra-tight formations. [Display omitted] • This study investigates H 2 permeability in organic-rich caprock in the subsurface. • It quantifies the effects of adsorption and slippage for H 2 in the nanosize conduit. • Slippage dominates H 2 flow, and the effects of adsorption are negligible. • H 2 conductance is higher than CH 4 conductance because H 2 adsorbs less to kerogen and slips more. • H 2 permeability is almost twice the CH 4 permeability in the organic-rich caprock. [ABSTRACT FROM AUTHOR]

Clean hydrogen is a promising option for reducing carbon dioxide emissions, but it has not yet been used as an energy carrier at the scale required for meeting the net-zero target by 2050. Hydrogen molecules are smaller than nitrogen and methane molecules. Hydrogen, nitrogen, and methane have densities of 0.09 g/L, 1.25 g/L, and 0.71 g/L, respectively, at the standard temperature and pressure. Our knowledge of the geological formations is based on responses to the larger and heavier gases; it is unclear whether we can apply this knowledge to store hydrogen at the required scale. We investigate the single-phase flow of hydrogen in the subsurface and compare it with the single-phase flows of nitrogen and methane. The comparison with nitrogen is helpful because it is used under laboratory conditions. The comparison with methane is also beneficial because engineers understand its behavior under in-situ conditions. We use the Knudsen number (Kn) to determine the flow behaviors under laminar conditions within two domains. The first is a permeable medium representing a conventional gas reservoir, and the second is caprock. Our study shows that the existing knowledge of the first domain's permeability applies to hydrogen flow; however, it is unrealistic for the second domain. The single-phase permeability of the caprock obtained by nitrogen in the laboratory underestimates hydrogen permeability at low pressures (<10 MPa), and the deviation is a non-linear function of pressure. Our study also shows that hydrogen permeability is always larger than methane permeability in the caprock. The difference between the two, controlled by the reservoir pressure, reached 70% in the caprock. The presented results have applications if hydrogen storage in gas reservoirs becomes a reality. • Hydrogen permeability is compared with those of nitrogen and methane. • Nitrogen permeability of caprock in the lab is smaller than hydrogen's at < 10 MPa. • Nitrogen permeability of caprock in the lab is larger than hydrogen's at > 15 MPa. • Hydrogen permeability of caprock is larger than methane's (max difference = 70%). • Hydrogen permeability is presented for the large storage for the net-zero target. [ABSTRACT FROM AUTHOR]

Highlights • We review the existing models for the critical properties (T c , P c) of gas in nano-size conduits. • We use the tree-like pore model to predict the critical properties of shale gas at the core scale. • The critical properties are determined by accounting for the pore structure and connectivity of shale formations in the United States. Abstract The transport properties of gas deviate from the nominal values, reported without confinements, when it is confined inside a nano-size conduit. This is because the interactions between the gas molecules and the conduit become more important than do those of the gas molecules with each other. The deviation is relevant to shale gas because of the ultra-narrow pore size in the matrix. With this in mind, we determine the critical temperature (T c) and critical pressure (P c) for shale formations in North America at the core scale. The shale formations are the Bakken, Barnett, Eagle Ford, Haynesville, Marcellus, Monterey, New Albany, Niobrara, Utica, Wolfcamp, and Woodford. The present study uses the acyclic pore model to account for the effective connectivity of shale samples at the core scale. It also differentiates between the pore-throat and pore-body size distributions. The former is used to derive the critical properties relevant to the fluid flow (displacement), and the latter is used to determine the effective properties relevant to the storage. Our study shows that the displacement-critical properties change significantly, whereas the storage-critical properties do not require modifications. Quantitative corrections of the critical properties for various formations are presented. The results have major applications in developing a realistic reservoir model for shale formations. [ABSTRACT FROM AUTHOR]

Highlights • We review slippage models for fluid (gas and liquid) flow in nano-size conduits. • We determine the effective slippage at the core scale for shale formations. • We determine the effective pore-throat size for slippage at the core scale in shale formations. Abstract A significant fraction of the pore-throat size in the matrix of a shale formation is smaller than 100 nm. Nanofluidics, a field that deals with the transport properties of sub-100-nm conduits, indicates that the fluid flow is enhanced for this range of pore-throat size. However, it is unclear how the slippage at the pore scale (single conduit) controls the effective slippage at the core scale (∼1 in.). The present study reviews the slippage models for the gas and liquid flows inside a single conduit based on the experimental and theoretical studies in the literature. It then investigates the effective enhancement in shale formations using an acyclic pore model, which represents the effective connectivity of the shale pore space at the core scale as it captures the mercury injection capillary pressure measurements (drainage). The effective slippage is presented in terms of governing parameters such as pore pressure and wettability. This study presents the effective pore-throat size, whose corresponding slippage is equal to the effective gas slippage at the core scale, for three shale samples. The numerical simulations indicate that the effective pore-throat size for the gas flow depends on the pore pressure. In addition, the measured permeability with liquid is higher than the nominal permeability, often referred to as the Hagen–Poiseuille model, with no slippage. The presented results have major implications for reservoir characterization based on standard petrophysical measurements. [ABSTRACT FROM AUTHOR]

Nanofluidics, which analyzes fluid transport through sub 100-nm conduits, has fascinated engineers in different fields and we petroleum engineers are no exception. This field gained a significant interest in petroleum engineering only when hydrocarbon production from shales became economically feasible. The basic transport properties of the fluid change for this range of conduit size. With this in mind, we analyze the effective gas viscosity of a shale at different pore pressures. Our objective is not to derive detailed information about the gas transport at a pore or a sub-pore scale, but rather to discuss the implications of pore-scale simulations on the effective gas viscosity at the core scale. We use an acyclic pore model to account for the effective connectivity of the pore space at the core scale. The acyclic model is physically representative because it can capture capillary pressure measurements of the drainage obtained from mercury intrusion experiments. We present the effective gas viscosity with respect to the nominal value, under unconfined conditions. Our analysis shows that the reported permeability in a pressure-driven flow has to be considered an effective transport property if nominal viscosity and density are used for interpretation. That is, we have to modify viscosity and permeability simultaneously in our reservoir model. Our study has major implications for building a realistic reservoir model for shales based on petrophysical measurements. [ABSTRACT FROM AUTHOR]

A better understanding of the transport properties of geothermal reservoirs will enable us to improve their energy recovery. With this in mind, we determine pore-body and pore-throat size distributions of The Geysers, which is the largest operating geothermal resource. We determine the former by modeling water adsorption and desorption, and the latter by investigating capillary pressure measurements for The Geysers samples. Our study is based on the acyclic pore model, which is physically representative of the matrix porosity. The matrix of rock is the finer grained mass that acts as a framework for larger grains. An integrated analysis of the petrophysical measurements helps us characterize the connected pore system of the formation more accurately because such measurements are sensitive to different aspects of the pore topology. [ABSTRACT FROM AUTHOR]

Existing conventional measurements face challenges in characterizing transport properties of a shale because they are designed originally for formations with relatively wide pores and high permeability. The integrated analysis of such measurements helps us better understand the connected pore system of a shale formation when they are sensitive to the pore topology and cover a wider range of pore size. Here, we analyze nitrogen adsorption–desorption and mercury intrusion measurements to characterize the pore space of a shale. We determine pore-body size distribution by interpreting adsorption–desorption experiments. We also calculate pore-throat size distribution from mercury intrusion. We adopt the acyclic pore model, which embraces limited pore connectivity, and account for the connected path of the pores at the core scale. Our study distinguishes the pore size relevant to the storage and the flow conductance for the shale. [ABSTRACT FROM AUTHOR]

We initiate pore-scale modeling of The Geysers to characterize the formation’s pore space. For this purpose, we analyze the drainage data obtained from mercury intrusion for different samples where the variation of the capillary pressure with wetting phase saturation shows a non-plateau-like trend. The non-plateau-like trend is inconsistent with cyclic pore models such as the regular lattice model, in which the random assignment of the pore size to a lattice results in a plateau-like variation of the capillary pressure with wetting phase in drainage. Our study reveals that we can capture the pore space of The Geysers using acyclic void models. The connectivity of pores is limited in acyclic models and there is only a single path between two pores when they are connected. To capture the pore space, we determine the number of pore throats required to model the drainage results. We also use the characterized acyclic models to analyze the single-phase flow behavior of The Geysers at pore scale. Our analysis of the single-phase permeability suggests that the fluid flow is controlled primarily by a small fraction of the pores whose characteristic sizes are notably larger than others, although the data are not sufficient to eliminate the possible contribution of other pores with smaller characteristic sizes. This study could have major implications for understanding transport phenomena in The Geysers at pore scale. [ABSTRACT FROM AUTHOR]

High-resolution images provide detailed information about pores whose characteristic sizes are usually on the order of few nanometers to micrometers in shales, but it remains challenging to relate the acquired information to the transport properties of a sample whose size is usually on the order of centimeters. It is not yet possible to determine the effective connectivity of the pore space at the core scale (∼1 cm) from high-resolution images. With this in mind, we analyze drainage experiments conducted on cores to interpret the topology of the connected path of the pore space at the core scale. Our study for different shales shows that the distance traveled inside the pore space—the length of the pore space—by the nonwetting phase at each capillary pressure is a fractal, unlike the pore volume, which is not necessarily a fractal. We determine the fractal dimensions for different shales and present two fractal models. This study can have major implications for understanding hydrocarbon transport in shales. [ABSTRACT FROM AUTHOR]

Pore connectivity is limited in shale formations, unlike in conventional reservoirs, for which cyclic void models, such as the regular-lattice model, are often used to represent the connectivity. In the cyclic models, the random assignment of throat sizes to lattice elements leads to a plateau-like variation of a capillary pressure with wetting phase saturation during a drainage displacement. Here, we develop acyclic void models in which the spatial distribution of throat sizes is not random. For certain spatial distributions these models yield a non-plateau-like drainage displacement. Such models thus provide more realistic representations of the void space in samples for which drainage experiments reveal the non-plateau-like trend of the capillary pressure versus saturation. Gas shales commonly show such a trend, and using the developed models, we predict the no-slip permeability of shale samples whose mercury intrusion capillary pressures curves were measured under confined boundary conditions. The predicted permeabilities are in good agreement with the lab measurements reported for these samples. Other models either fail to account for the non-plateau-like trend of the drainage as they adopt a random pore size distribution or they overestimate the no-slip permeability for saturated flow. The models developed here could have applications in other porous media whose drainage data do not exhibit a plateau-like variation. [ABSTRACT FROM AUTHOR]

Abstract: Vibrational analysis of single-walled carbon nanotubes (SWCNTs) is performed using a finite element method (FEM). To this end, the vibrational behavior of bridge and cantilever SWCNTs with different side lengths and diameters is modeled by three-dimensional elastic beams and point masses. The beam element elastic properties are calculated by considering mechanical characteristics of the covalent bonds between the carbon atoms in the hexagonal lattice. The mass of each beam element is assumed as point masses at nodes coinciding with the carbon atoms. Implementing the atomistic simulation approach, the natural frequencies of zigzag and armchair SWCNTs are computed. It is observed that the findings are in good agreement with the molecular structural mechanics data available in the literature. Then, the computational results are adopted to develop a predictive equation to propose a quick tool for estimating natural frequencies of the SWCNTs with different boundary conditions and geometrical parameters. [Copyright &y& Elsevier]

Abstract: An atomistic simulation method is adopted to investigate the elastic characteristics of defect-free single-layered graphene sheet (SLGS). To this end, the equivalent structural beam is employed to model interatomic forces of the covalently bonded carbon atoms. The beam properties are computed by considering the covalent bond stiffnesses. To calculate the Young’s modulus, shear modulus and Poisson’s ratio of the SLGS, the equivalent continuum sheet model is proposed and the effect of chirality on the SLGS elastic properties is examined. It is perceived that there exists a good agreement between the atomistic modeling results and the data available in the literature. [Copyright &y& Elsevier]

Abstract: Molecular structural mechanics is implemented to investigate the vibrational characteristics of defect-free single-layered graphene sheets (SLGSs), which have potential applications as strain sensors. The effect of strain on the fundamental frequencies of the defect-free zigzag and armchair models with clamped–clamped boundary condition is studied. The atomistic modeling results reveal while sensitivities of the strain sensors are not influenced significantly by chirality, they can be slightly increased by decreasing aspect ratios of the sheets. It is further shown that the SLGSs-based strain sensors are more sensitive to the applied stretch than the SWCNTs versions. [Copyright &y& Elsevier]

Abstract: Molecular structural mechanics is implemented to model the vibrational behavior of defect-free single-layered graphene sheets (SLGSs) at constant temperature. To mimic these two-dimensional layers, zigzag and armchair models with cantilever and bridge boundary conditions are adopted. Fundamental frequencies of these nanostructures are calculated, and it is perceived that they are independent of the chirality and aspect ratio. The effects of point mass and atomistic dust on the fundamental frequencies are also considered in order to investigate the possibility of using SLGSs as sensors. The results show that the principal frequencies are highly sensitive to an added mass of the order of . [Copyright &y& Elsevier]

Although the Middle East's carbonate reservoirs were the first and most studied rocks in the world, Middle Eastern shale reservoirs are still poorly understood compared with other unconventional formations in the US. We investigate the pore-throat size and pore-body size distributions of Midra shale in Qatar to quantify the pore-scale features that control transport properties at the core scale. We measured the capillary pressure by injecting mercury into samples in drainage. The capillary pressure variation with wetting phase saturation exhibits a plateau-like trend, which differs from the linear trend observed in most shales in the US. The capillary pressure measurements quantify the pore-throat size distribution. We also measure nitrogen adsorption and analyze the measurements to determine the pore-body size distribution. This study shows that the pore-throat size has a narrow distribution, and its average is close to 22 nm. In addition, the pore-body size has a wide distribution, and its average is 18 nm. Thus, the transport properties dependent on the pore-throat size require modifications to account for the pore proximity to represent subsurface conditions. The transport properties, such as density, relevant to the pore volume in the matrix can be estimated with reasonable accuracy from the gas composition in wider conduits. The presented results have applications for the development of unconventional gas, which is the cleanest fossil fuel. • We conduct a comprehensive investigation of a tight formation. • We investigate the geology of a formation. • The pore-throat size distribution is measured and analyzed. • The pore-body size distribution is measured and analyzed. • We compare the two distributions, and discuss their effects on the transport properties. [ABSTRACT FROM AUTHOR]

The existing models for fracture toughness characterization based on nanoindentations that account for the fracture length are limited to simple (ideal) geometries that are absent in shales. The present study proposes two conceptual models to estimate the fracture length created by nanoindentations in shales. It also presents a workflow to apply the conceptual models and uses machine learning, enabling a systematic and automated analysis. The conceptual models assume that the induced fracture is in the first mode to determine the fracture toughness. In this study, fracture toughness is also determined by the energy method that relates the load-displacement hysteresis to the fracture toughness without restricting the fracture mode. The present study sheds light on the complexities of characterizing fracture toughness using nanoindentations and has applications in the petroleum industry. The conceptual models are appealing for formation characterization using small pieces, such as drill cuttings, when large samples (~2.5 cm) required for conventional tests are unavailable. The conceptual models have applications in estimating fracture toughness when the induced fracture patterns become more complex. • We predict the fracture toughness of a shale sample using machine learning. • Nanoindentation is used to create sub-100-micromillimeter fractures. • Conceptual models are presented to quantify the fracture length. • The fracture length is interpreted from high-resolution images. [ABSTRACT FROM AUTHOR]

It is imperative to characterize the formation permeability to simulate the flow behavior at subsurface conditions. An accurate characterization at the core scale is possible when large samples are available, but often this is not the case, as such samples are hard to recover. Instead, drill cuttings (small pieces) are usually the only source available, especially in real-time conditions. Thus, mercury injection capillary pressure measurements, which are applicable to small pieces, have been used to infer the formation permeability. The challenge is that capillary pressure measurements entail further interpretations, as they can be converted to the pore-throat size distribution but not directly to the permeability. Thus, researchers have proposed different empirical and theoretical relations to predict the permeability. The present study uses machine learning, a data-driven approach, to predict carbonate formation permeability. The data-driven approach does not impose any restriction on the spatial distribution of the pore-throat sizes in the network of connected pores, but rather trains models based on the existing data. The present study is based on 193 carbonate samples whose data (porosity, permeability, and mercury injection capillary pressure measurements) are available in the literature. The permeability values vary from nanodarcies to darcies. We propose two new correlations, with and without grouping analysis, for permeability prediction. The results are promising, as the averaged R 2 score obtained with 50 iterations is larger than 0.96. The study provides a valuable tool for permeability prediction based on numerical methods that distinguish the pore structure by taking into account underlying trends in the measurements. • We predict carbonate formation permeability using machine learning. • Formation permeability is predicted for 193 samples from the U.S. and the Middle East. • The averaged R 2 score obtained with 50 iterations is larger than 0.96 for all the samples. • The formation permeability is predicted at the core scale based on mercury injection capillary pressure measurements. [ABSTRACT FROM AUTHOR]