Methane Diffusion in a Flexible Kerogen Matrix

Role of Adsorption-Induced Deformation on Gas Self-Diffusivity in a Flexible Microporous Coal Matrix

Adsorption-induced deformation has long been underappreciated in gas transport studies of microporous coal, yet it strongly influences pore configurations and diffusive pathways. Here, a hybrid grand canonical Monte Carlo (GCMC)/molecular dynamics (MD) approach and equilibrium MD (EMD) simulations are employed to investigate how matrix flexibility reshapes pore structures and, in turn, impacts CH4 and CO2 self-diffusion in connected pore networks under various gas loadings. The results show that coal matrix deformation enhances adsorption, with CO2 exhibiting greater uptake and volumetric strain than CH4. A universal linear relationship emerges among gas loading, free volume ratio, and self-diffusion coefficients for both rigid and flexible matrices. In flexible matrices, this linearity features a gentler slope, indicating reduced diffusion sensitivity to diminishing free volume with loadings. By comparing geometrical and effective tortuosity, it is revealed that strongly adsorbing CO2 induces significant swelling and complex local rearrangements at elevated loadings, pushing geometrical tortuosity far beyond rigid-matrix levels, whereas CH4─with weaker adsorption─drives smaller, more uniform structural adjustments that only mildly increase geometrical tortuosity. These differences in tortuosity directly reflect changes in path complexity, which in turn governs self-diffusion behavior. Collectively, the findings clarify the dynamic coupling between gas adsorption, matrix deformation, and self-diffusivity in microporous coal, offering critical guidance for enhanced gas recovery and CO2 sequestration strategies that rely on accurate modeling of gas transport in deformable media.

Adsorption-Induced Deformation in Microporous Kerogen by Hydrogen and Methane: Implications for Underground Hydrogen Storage

Accurately assessing the adsorption and diffusion behaviors of H2, CH4, and their mixtures are essential for estimating underground hydrogen storage (UHS). This understanding is critical for the safe and efficient storage of H2 in depleted shale gas reservoirs. Although H2 adsorption in kerogen has been extensively studied, adsorption-induced swelling remains unexplored in UHS. In this study, we investigate adsorption mechanisms using Lagrangian and Eulerian approaches and analyze diffusion in kerogen through molecular simulations. Our results reveal that in the presence of cushion gases like CH4, which exhibit stronger adsorption than H2, neglecting kerogen deformation can lead to an underestimation of storage capacity by approximately 40%. Furthermore, increasing pressure makes H2 adsorption behavior deviate from the consistent swelling trend that is observed with CH4, with kerogen either swelling or contracting depending on the pore size. Simulations also predict that H2 self-diffusion coefficient in porous kerogen is 1 order of magnitude higher than CH4. These findings highlight the importance of incorporating kerogen flexibility into the modeling of UHS involving multiple gas species to improve the accuracy and safety of H2 storage operations in shale reservoirs.

Confined fluid dynamics in a viscoelastic, amorphous, and microporous medium: Study of a kerogen by molecular simulations and the generalized Langevin equation

We combine the use of molecular dynamics simulations and the generalized Langevin equation to study the diffusion of a fluid adsorbed within kerogen, the main organic phase of shales. As a class of microporous and amorphous materials that can exhibit significant adsorption-induced swelling, the dynamics of the kerogen's microstructure is expected to play an important role in the confined fluid dynamics. This role is investigated by conducting all-atom simulations with or without solid dynamics. Whenever the dynamics coupling between the fluid and solid is accounted for, we show that the fluid dynamics displays some qualitative differences compared to bulk fluids, which can be modulated by the amount of adsorbed fluid owing to adsorption-induced swelling. We highlight that working with the memory kernel, the central time correlation function of the generalized Langevin equation, allows the fingerprint of the dynamics of the solid to appear on that of the fluid. Interestingly, we observe that the memory kernels of fluid diffusion in kerogen qualitatively behave as those of tagged particles in supercooled liquids. We emphasize the importance of reproducing the velocity-force correlation function to validate the memory kernel numerically obtained as confinement enhances the numerical instabilities. This route is interesting as it opens the way for modeling the impact of fluid concentration on the diffusion coefficient in such ultra-confining cases.

Dependence of Methane Transport on Pore Informatics in the Amorphous Nanoporous Kerogen Matrix

Fluid transport in kerogen is mainly diffusion-driven, while its dependence on pore informatics is still poorly understood. It is challenging for experiments to identify the effect of pore informatics (such as pore connectivity and tortuosity) on fluid transport therein. Therefore, in this work, we use molecular dynamics simulations to study methane transport behaviors in amorphous kerogen matrices with broad pore properties. The pore properties including porosity, pore connectivity, pore size, and diffusive tortuosity are characterized. Next, self-diffusion coefficients in the connected pores (DeffS) and in the total pores without distinguishing its connectivity (DtotS) are calculated in all the kerogen matrices based on the free volume theory. We find that both DeffS and DtotS exponentially decreases with methane loading with two controlled parameters: fitting constant αeff and DeffS(0) (DeffS at infinitely small loading) for DeffS and fitting constant αtot and DtotS(0) (DtotS at infinitely small loading) for DtotS. However, in the kerogen models with relatively low pore connectivity, αeff and αtot as well as DeffS(0) and DtotS(0) can be quite different, inducing the different estimations of DeffS and DtotS. Since methane in the unconnected pores does not contribute to the actual transport, it is important to recognize connected pores when evaluating the fluid transport in kerogen. On the other hand, DeffS(0) strongly depends on the effective limiting pore size (rlim_eff) of the dominant flow path and effective diffusive tortuosity (τeff), in which DeffS(0) linearly increases with (rlim_eff/τeff)2. We also find that αeff is a multivariable function of ϕeff, τeff, and rlim_eff, but their generalized relation requires more data to obtain. This work provides important insights into fluid transport in kerogen based on the kerogen pore informatics, which are important to shale gas development.

Molecular Simulation of Argon Adsorption and Diffusion in a Microporous Carbon with Poroelastic Couplings

Neglected for a long time in molecular simulations of fluid adsorption and transport in microporous carbons, adsorption-induced deformations of the matrix have recently been shown to have important effects on both sorption isotherms and diffusion coefficients. Here we investigate in detail the behavior of a recently proposed 3D-connected mature kerogen model, as a generic model of aromatic microporous carbon with atomic H/C ∼ 0.5, in both chemical and mechanical equilibrium with argon at 243 K over an extended pressure range. We show that under these conditions the material exhibits some viscoelasticity, and simulations of hundreds of nanoseconds are required to accurately determine the equilibrium volumes and sorption loadings. We also show that neglecting matrix internal deformations and swelling can lead to underestimations of the loading by up to 19% (swelling only) and 28% (swelling and internal deformations). The volume of the matrix is shown to increase up to about 8% at the largest pressure considered (210 MPa), which induces an increase of about 33% of both pore volume and specific surface area via the creation of additional pores, yet does not significantly change the normalized pore size distribution. Volume swelling is also rationalized by using a well-known linearized microporomechanical model. Finally, we show that self-diffusivity decreases with applied pressure, following an almost perfectly linear evolution with the free volume. Quantitatively, neglecting swelling and internal deformations tends to reduce the computed self-diffusivities.

On the role of history-dependent adsorbate distribution and metastable states in switchable mesoporous metal-organic frameworks

A unique feature of metal-organic frameworks (MOFs) in contrast to rigid nanoporous materials is their structural switchabilty offering a wide range of functionality for sustainable energy storage, separation and sensing applications. This has initiated a series of experimental and theoretical studies predominantly aiming at understanding the thermodynamic conditions to transform and release gas, but the nature of sorption-induced switching transitions remains poorly understood. Here we report experimental evidence for fluid metastability and history-dependent states during sorption triggering the structural change of the framework and leading to the counterintuitive phenomenon of negative gas adsorption (NGA) in flexible MOFs. Preparation of two isoreticular MOFs differing by structural flexibility and performing direct in situ diffusion studies aided by in situ X-ray diffraction, scanning electron microscopy and computational modelling, allowed assessment of n-butane molecular dynamics, phase state, and the framework response to obtain a microscopic picture for each step of the sorption process.

Interfacial Adsorption Kinetics of Methane in Microporous Kerogen

Rapid declines in unconventional shale production arise from the poorly understood interplay between gas transport and adsorption processes in microporous organic rock. Here, we use high-fidelity molecular dynamics (MD) simulations to resolve the time-varying adsorption of methane gas in realistic organic rock samples, known as kerogen. The kerogen samples derive from various geological shale fields with porosities ranging between 20% and 50%. We propose a kinetics sorption model based on a generalized solution of diffusive transport inside a nanopore to describe the adsorption kinetics in kerogen, which gives excellent fits with all our MD results, and we demonstrate it scales with the square of the length of kerogen. The MD adsorption time constants for all samples are compared with a simplified theoretical model, which we derive from the Langmuir isotherm for adsorption capacitance and the free-volume theory for steady, highly confined bulk transport. While the agreement with the MD results is qualitatively very good, it reveals that, in the limit of low porosity, the diffusive transport term dominates the characteristic time scale of adsorption, while the adsorption capacitance becomes important for higher pressures. This work provides the first data set for adsorption kinetics of methane in kerogen, a validated model to accurately describe this process, and a qualitative model that links adsorption capacitance and transport with the adsorption kinetics. Furthermore, this work paves the way to upscale interfacial adsorption processes to the next scale of gas transport simulations in mesopores and macropores of shale reservoirs.

Nanoscale Accessible Porosity as a Key Parameter Depicting the Topological Evolution of Organic Porous Networks

A significant part of the hydrocarbons contained in source rocks remains confined within the organic matter-called kerogen-from where they are generated. Understanding the sorption and transport properties of confined hydrocarbons within the kerogens is, therefore, paramount to predict production. Specifically, knowing the impact of thermal maturation on the evolution of the organic porous network is key. Here, we propose an experimental procedure to study the interplay between the chemical evolution and the structural properties of the organic porous network at the nanometer scale. First, the organic porous networks of source rock samples, covering a significant range of natural thermal maturation experienced by the Vaca Muerta formation (Neuquén Basin, Argentina), are physically reconstructed using bright-field electron tomography. Their structural description allows us to measure crucial parameters such as the porosity, specific pore volume and surface area, aperture and cavity size distributions, and constriction. In addition, a model-free computation of the topological properties (effective porosity, connectivity, and tortuosity) is conducted. Overall, we document a general increase of the specific pore volume with thermal maturation. This controls the topological features depicting increasing accessibility to alkane molecules, sensed by the evolution of the effective porosity. Collectively, our results highlight the input of bright-field electron tomography in the study of complex disordered amorphous porous media, especially to describe the interplay between the structural features and transport properties of confined fluids.

Effect of Kerogen Maturity, Water Content for Carbon Dioxide, Methane, and Their Mixture Adsorption and Diffusion in Kerogen: A Computational Investigation

The adsorption behavior of CO₂, CH₄, and CO₂/CH₄ mixtures in four different mature kerogens in the absence/presence of water was studied using grand canonical Monte Carlo and classical molecular dynamics methods. The results exhibit that the adsorption isotherms of single-component CO₂ or CH₄ in kerogen present similar trends and show type I Langmuir adsorption behavior according to the IUPAC classification; the total adsorbed amount of both gases follows the order of type II-A < type II-B < type II-C < type II-D kerogen under the same conditions. The changing behavior of isosteric heat decreases first and then increases, which can explain the heterogeneous characteristic of the kerogen pore surface. The Coulombic and van der Waals interactions between CO₂ and kerogens play an important role on adsorption, while for CH₄ adsorption, the electrostatic effect is very small, even negligible. The N-, S-, and O-containing groups in kerogen have more remarkable influence on adsorption of CO₂ than CH₄ because of their strong adsorption energy, therefore notably improving the selectivity of CO₂ over CH₄ and following the order of type II-A > type II-B > type II-C > type II-D, which is beneficial to carbon capture and storage. Both pressure and temperature have an obvious impact on gas molecule diffusion, and low pressure and high temperature correspond to a large diffusion coefficient. In addition, preabsorbed water has a negative effect on the adsorption of CO₂/CH₄, and for the same amount of water molecules, the effect follows the order of type II-A > type II-B > type II-C > type II-D kerogens. The binding energy of water-kerogen is stronger than that of pure CH₄ or CO₂-kerogen. The selectivity of CO₂ over CH₄ on kerogen increases with an increasing water content.