Subcontinuum mass transport of condensed hydrocarbons in nanoporous media

Operando scanning electron microscopy platform for in situ imaging of fluid evolution in nanoporous shale

Fluid-solid interactions in nanoporous materials underlie processes fundamental to natural and engineered processes, including the thermochemical transformation of argillaceous materials during high-level nuclear waste disposal. Operando fluid-solid resolution at the nanoscale, however, is still not possible with existing optical and electron microscopy approaches that are constrained by the diffraction limit of light and by vacuum-fluid incompatibility, respectively. In this work, we develop an operando scanning electron microscopy (SEM) platform that enables the first direct in situ imaging of dynamic fluid-solid interactions in nanoporous materials with spatio-temporal-chemical resolutions of ∼2.5 nm per pixel and 10 fps, along with elemental distributions. Using this platform, we reveal necessary conditions for thermochemical pore and fracture generation in shales and measure their surface wetting characteristics that constrain the feasibility of high-level nuclear waste containment. Notably, we show that low heating-rate conditions typical of radioactive decay produce hydrocarbon liquids that wet fracture and pore surfaces in a self-sealing manner to impede aqueous radionuclide advection.

Colloid Transport in Bicontinuous Nanoporous Media

Colloid transport and retention in porous media are critical processes influencing various Earth science applications, from groundwater remediation to enhanced oil recovery. These phenomena become particularly complex in the confined spaces of nanoporous media, where strong boundary layer effects and nanoconfinement significantly alter colloid behavior. In this work, we use particle dynamics models to simulate colloid transport and retention processes in bicontinuous nanoporous (BNP) media under pressure gradients. By utilizing particle-based models, we track the movement of each colloid and elucidate the underlying colloid retention mechanisms. Under unfavorable attachment conditions, the results reveal two colloid retention mechanisms: physical straining and trapping in low-flow zone. Furthermore, we investigate the effects of critical factors including colloid volume fraction, d, pressure difference, ΔP, interaction between colloids and BNP media, Ec-p, and among colloids, Ec-c, on colloid transport. Analysis of breakthrough curves and colloid displacements demonstrates that higher values of d, lower values of ΔP, and strong Ec-p attractions significantly increase colloid retention, which further lead to colloid clogging and jamming. In contrast, Ec-c has minimal impact on colloid transport due to the limited colloid-colloid interaction in nanoporous channels. This work provides critical insights into the fundamental factors governing colloid transport and retention within stochastic nanoporous materials.

Competitive sorption of CO2/CH4 and CO2 capture on modified silica surfaces: A molecular simulation

The effect of functionalization of modified silica (FMS) surfaces on the adsorption behaviors for CH4, CO2 and the mixture have been studied by combining a grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) methods. The isotherms, gas distribution, sorption sites, isosteric heat, interaction energy and adsorption selectivity for CO2/CH4 mixture are computed and discussed. And the effects of pressure and temperature on adsorption behavior are also studied. The adsorption capacity (C) of surface with various functional groups for CH4 is as follows: C(SiO2-COOH) > C(SiO2-SH) > C(SiO2-OH) > C(SiO2-CH3) > C(SiO2-NH2) > C(SiO2-H) and for CO2 is as follows: C(SiO2-COOH) > C(SiO2-SH) > C(SiO2-NH2) > C(SiO2-OH) > C(SiO2-CH3) > C(SiO2-H). Increasing temperature is not advantageous for gas adsorption on all FMS surfaces. The CO2/CH4 selectivity (S) for FMS surfaces decrease in the following order of S(SiO2-COOH) > S(SiO2-NH2) > S(SiO2-OH) > S(SiO2-SH) > S(SiO2-CH3) > S(SiO2-H). As the pressure increase, the CO2/CH4 selectivity decrease early and then flatten out to a constant value. The isosteric heat of adsorption (Qst) for gas adsorbed on each FMS surface are also calculated, the value of isosteric heat for CO2 is much higher than that for CH4 due to the stronger interaction between CO2 molecules and functional groups of FMS surface. The result of the smallest self-diffusion coefficients of gas in SiO2-COOH slit pores is consistent with the adsorption capacity in the slit pore with corresponding functional group. The electronegative atoms in the functional group act as basic adsorption sites for gas adsorbate molecules, which generates a larger electrostatic contribution on the selectivity of CO2 over CH4.

On De Gennes narrowing of fluids confined at the molecular scale in nanoporous materials

Beyond well-documented confinement and surface effects arising from the large internal surface and severely confining porosity of nanoporous hosts, the transport of nanoconfined fluids remains puzzling in many aspects. With striking examples such as memory, i.e., non-viscous effects, intermittent dynamics, and surface barriers, the dynamics of fluids in nanoconfinement challenge classical formalisms (e.g., random walk, viscous/advective transport)-especially for molecular pore sizes. In this context, while molecular frameworks such as intermittent Brownian motion, free volume theory, and surface diffusion are available to describe the self-diffusion of a molecularly confined fluid, a microscopic theory for collective diffusion (i.e., permeability), which characterizes the flow induced by a thermodynamic gradient, is lacking. Here, to fill this knowledge gap, we invoke the concept of "De Gennes narrowing," which relates the wavevector-dependent collective diffusivity D0(q) to the fluid structure factor S(q). First, using molecular simulation for a simple yet representative fluid confined in a prototypical solid (zeolite), we unravel an essential coupling between the wavevector-dependent collective diffusivity and the structural ordering imposed on the fluid by the crystalline nanoporous host. Second, despite this complex interplay with marked Bragg peaks in the fluid structure, the fluid collective dynamics is shown to be accurately described through De Gennes narrowing. Moreover, in contrast to the bulk fluid, the departure from De Gennes narrowing for the confined fluid in the macroscopic limit remains small as the fluid/solid interactions in severe confinement screen collective effects and, hence, weaken the wavevector dependence of collective transport.

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 Insights into the Salinity Effects on Movability of Oil-Brine in Shale Nanopore-Throat Systems

Low-salinity flooding has been well recognized as a promising strategy to increase shale oil recovery, but the underlying mechanism remains unclarified, especially for complex nanopore networks filled with oil-brine fluids. In this study, the pressure-driven flow of an oil-brine fluid with varying salinities in shale nanopore-throat channels was first investigated based on molecular dynamics simulations. The critical pressure driving oil to intrude into a nanothroat filled with brine of varying salinities was determined. Simulation results indicate that the salinity of brine exhibits great effects on the movability of oil, and low salinity favors the increase of oil movability. Further analysis of the interactions between fluid and pore walls as well as the displacement pressures reveals dual effects of brine salinity on oil transportation in a nanopore-throat. On the one hand, hydrated cations anchoring onto throat walls enlarge the effective flow width in the throat before the hydration complexes reach the maximum. On the other hand, the interfacial tension between oil and brine increases with the brine salinity, which increases the capillary resistance and leads to a higher displacement pressure. These findings highlight the effects of brine salinity on oil movability in a nanopore-throat, which will promote the understanding of oil accumulation and dissipation in petroleum systems, as well as help to develop enhanced oil recovery.

Nanoscale Prediction of the Thermal, Mechanical, and Transport Properties of Hydrated Clay on 106- and 1015-Fold Larger Length and Time Scales

Coupled thermal, hydraulic, mechanical, and chemical (THMC) processes, such as desiccation-driven cracking or chemically driven fluid flow, significantly impact the performance of composite materials formed by fluid-mediated nanoparticle assembly, including energy storage materials, ordinary Portland cement, bioinorganic nanocomposites, liquid crystals, and engineered clay barriers used in the isolation of hazardous wastes. These couplings are particularly important in the isolation of high-level radioactive waste (HLRW), where heat generated by radioactive decay can drive the temperature up to at least 373 K in the engineered barrier. Here, we use large-scale all-atom molecular dynamics simulations of hydrated smectite clay nanoparticle assemblages to predict the fundamental THMC properties of hydrated compacted clay over a wide range of temperatures (up to 373 K) and dry densities relevant to HLRW management. Equilibrium simulations of clay-water mixtures at different hydration levels are analyzed to quantify material properties, including thermal conductivity, heat capacity, thermal expansion, suction, water and ion self-diffusivity, and hydraulic conductivity. Predictions are validated against experimental results for the properties of compacted bentonite clay. Our results demonstrate the feasibility of using atomistic-level simulations of assemblages of clay nanoparticles on scales of tens of nanometers and nanoseconds to infer the properties of compacted bentonite on scales of centimeters and days, a direct upscaling over 6 orders of magnitude in space and 15 orders of magnitude in time.

The validity of the continuum modeling limit in a single pore flows to the molecular scale

The discrete characteristics of molecules become dominant in the molecular regime when the surface-to-volume ratio becomes very high. Using the well-established continuum approach is questionable due to this dominant behavior. Due to the lack of perfect modeling of such a small-scale system, the experimentalist must rely on the trial and error method. Here we analyze the water transport mechanism through a nanoporous graphene membrane at the molecular level by adopting the classical molecular dynamics (MD) simulation. The results for SPC/E water molecules were compared with those obtained for liquid argon atoms and continuum Sampson's equation predictions. We find that the effect of local variants such as density layering, interatomic forces, slip velocity, and geometric boundary conditions become exponentially dominant with decreasing nanopore size. Consequently, the continuum assumptions break down at 1.5 nm pore diameter due to neglecting the dominant local properties.

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.

Insights into the 3D permeable pore structure within novel monodisperse mesoporous silica nanoparticles by cryogenic electron tomography

Sintered agglomerate of synthetic mesoporous silica nanoparticles (MSNs) is an architected geomaterial that provides confinement-mediated flow and transport properties of fluids needed for environmental research such as geological subsurface energy storage or carbon capture. The design of those properties can be guided by numerical simulations but is hindered by the lack of method to characterize the permeable pores within MSNs due to pore size. This work uses the advances of an Individual Particle cryogenic transmission Electron Tomography (IPET) technique to obtain detailed 3D morphology of monodispersed MSNs with diameters below 50 nm. The 3D reconstructed density-maps show the diameters of those MSNs vary from 35-46 nm, containing connected intraparticle pores in diameter of 2-20 nm with a mean of 9.2 ± 3 nm, which is comparable to the mean interparticle pore diameters in sintered agglomerate. The characterization of the pore shape and dimensions provides key information for estimating the flow and transport properties of fluids within the sintered agglomerate of those MSNs and for modeling the atomic MSN structures needed for pore-fluid simulations.

Machine Learning Predictions of Simulated Self-Diffusion Coefficients for Bulk and Confined Pure Liquids

Diffusion properties of bulk fluids have been predicted using empirical expressions and machine learning (ML) models, suggesting that predictions of diffusion also should be possible for fluids in confined environments. The ability to quickly and accurately predict diffusion in porous materials would enable new discoveries and spur development in relevant technologies such as separations, catalysis, batteries, and subsurface applications. In this work, we apply artificial neural network (ANN) models to predict the simulated self-diffusion coefficients of real liquids in both bulk and pore environments. The training data sets were generated from molecular dynamics (MD) simulations of Lennard-Jones particles representing a diverse set of 14 molecules ranging from ammonia to dodecane over a range of liquid pressures and temperatures. Planar, cylindrical, and hexagonal pore models consisted of walls composed of carbon atoms. Our simple model for these liquids was primarily used to generate ANN training data, but the simulated self-diffusion coefficients of bulk liquids show excellent agreement with experimental diffusion coefficients. ANN models based on simple descriptors accurately reproduced the MD diffusion data for both bulk and confined liquids, including the trend of increased mobility in large pores relative to the corresponding bulk liquid.

Insights into Waterflooding in Hydrocarbon-Bearing Nanochannels of Varying Cross Sections from Mesoscopic Multiphase Flow Simulations

Waterflooding is one of the geotechniques used to recover fuel sources from nanoporous geological formations. The scientific understanding of the process that involves the multiphase flow of nanoconfined fluids, however, has lagged, mainly due to the complex nanopore geometries and chemical compositions. To enable the benchmarked flow of nanoconfined fluids, architected geomaterials, such as synthesized mesoporous silica with tunable pore shapes and surface chemical properties, are used for designing and conducting experiments and simulations. This work uses a modified many-body dissipative particle dynamics (mDPD) model with accurately calibrated parameters to perform parametric flow simulations for studying the influences of waterflooding-driven power, pore shape, surface roughness, and surface wettability on the multiphase flow in heptane-saturated silica nanochannels. Remarkably, up to an 80% reduction in the effective permeability is found for water-driven heptane flow in a baseline 4.5-nm-wide slit channel when compared with the Hagen-Poiseuille equation. In the 4.5-nm-wide channels with architected surface roughness, the flow rate is found to be either higher or lower than the baseline case, depending on the shape and size of cross sections. High wettability of the solid surface by water is essential for achieving a high recovery of heptane, regardless of surface roughness. When the solid surface is less wetting or nonwetting to water, the existence of an optimal waterflooding-driven power is found to allow for the highest possible recovery. A detailed analysis of the evolution of the transient water-heptane interface in those nanochannels is presented to elucidate the underlying mechanisms that impact or dictate the multiphase flow behaviors.

Hierarchical triphase diffusion photoelectrodes for photoelectrochemical gas/liquid flow conversion

Photoelectrochemical device is a versatile platform for achieving various chemical transformations with solar energy. However, a grand challenge, originating from mass and electron transfer of triphase-reagents/products in gas phase, water/electrolyte/products in liquid phase and catalyst/photoelectrode in solid phase, largely limits its practical application. Here, we report the simulation-guided development of hierarchical triphase diffusion photoelectrodes, to improve mass transfer and ensure electron transfer for photoelectrochemical gas/liquid flow conversion. Semiconductor nanocrystals are controllably integrated within electrospun nanofiber-derived mat, overcoming inherent brittleness of semiconductors. The mechanically strong skeleton of free-standing mat, together with satisfactory photon absorption, electrical conductivity and hierarchical pores, enables the design of triphase diffusion photoelectrodes. Such a design allows photoelectrochemical gas/liquid conversion to be performed continuously in a flow cell. As a proof of concept, 16.6- and 4.0-fold enhancements are achieved for the production rate and product selectivity of methane conversion, respectively, with remarkable durability.

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.

Sorption-Deformation-Percolation Model for Diffusion in Nanoporous Media

Diffusion of molecules in porous media is a critical process that is fundamental to numerous chemical, physical, and biological applications. The prevailing theoretical frameworks are challenged when explaining the complex dynamics resulting from the highly tortuous host structure and strong guest-host interactions, especially when the pore size approximates the size of diffusing molecule. This study, using molecular dynamics, formulates a semiempirical model based on theoretical considerations and factorization that offer an alternative view of diffusion and its link with the structure and behavior (sorption and deformation) of material. By analyzing the intermittent dynamics of water, microscopic self-diffusion coefficients are predicted. The apparent tortuosity, defined as the ratio of the bulk to the confined self-diffusion coefficients, is found to depend quantitatively on a limited set of material parameters: heat of adsorption, elastic modulus, and percolation probability, all of which are experimentally accessible. The proposed sorption-deformation-percolation model provides guidance on the understanding and fine-tuning of diffusion.

Effect of Nanoconfinement on NMR Relaxation of Heptane in Kerogen from Molecular Simulations and Measurements

Kerogen-rich shale reservoirs will play a key role during the energy transition, yet the effects of nanoconfinement on the NMR relaxation of hydrocarbons in kerogen are poorly understood. We use atomistic MD simulations to investigate the effects of nanoconfinement on the ¹H NMR relaxation times T₁ and T₂ of heptane in kerogen. In the case of T₁, we discover the important role of confinement in reducing T₁ by ∼3 orders of magnitude from that of bulk heptane, in agreement with measurements of heptane dissolved in kerogen from the Kimmeridge Shale, without any models or free parameters. In the case of T₂, we discover that confinement breaks spatial isotropy and gives rise to residual dipolar coupling which reduces T₂ by ∼5 orders of magnitude from the value for bulk heptane. We use the simulated T₂ to calibrate the surface relaxivity and thence predict the pore-size distribution of the organic nanopores in kerogen, without additional experimental data.

Breakthrough pressure of oil displacement by water through the ultra-narrow kerogen pore throat from the Young-Laplace equation and molecular dynamic simulations

As one common unconventional reservoir, shale plays a pivotal role to compensate the depletion of conventional oil resources. There are numerous nanoscale pores and ultra-narrow pore throats (sub 2 nm) in shale media. To displace oil through ultra-narrow pore throats by water, one needs to overcome excessively-high capillary pressure. Understanding the water-oil two-phase displacement process through pore throats is critical to numerical simulation on tight/shale oil exploitation and ultimate oil recovery estimation. In this work, we use molecular dynamics simulations to investigate oil (represented by n-octane) displacement by water through a ~2 nm kerogen (represented by Type II-C kerogen) pore throat. Besides, the applicability of the Young-Laplace equation to the ultra-narrow kerogen pore throat has been assessed. We find that although the Type II-C kerogen is generally oil-wet, water has an excellent displacement efficiency without the oil film on the substrate, thanks to the hydrogen bonding formed between water and heteroatoms (such as O, N, and S) on the kerogen surface. Unlike previous studies, the capillary pressure obtained from the widely used Young-Laplace equation shows a good agreement with the breakthrough pressure obtained from MD simulations for the ∼2 nm kerogen pore throat. Our work indicates that explicitly considering intermolecular interactions as well as atomistic and molecular level characteristics is imperative to study the two-phase displacement process through ultra-narrow pore throats.

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. 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.

Two-step diffusion in cellular hygroscopic (vascular plant-like) materials

Vascular plants, a vast group including conifers, flowering plants, etc., are made of a cellular hygroscopic structure containing water in the form of either free (i.e., in a standard liquid state) or bound (i.e., absorbed in the cell walls) water. From nuclear magnetic resonance techniques, we distinguish the dynamics of bound water and free water in a typical material (softwood) with such a structure, under convective drying. We show that water extraction relies on two mechanisms of diffusion in two contiguous regions of the sample, in which respectively the material still contains free water or only contains bound water. However, in any case, the transport is ensured by bound water. This makes it possible to prolong free water storage despite dry external conditions and shows that it is possible to extract free water in depth (or from large heights) without continuity of the free water network.

Molecular size-dependent subcontinuum solvent permeation and ultrafast nanofiltration across nanoporous graphene membranes

Selective solvent and solute transport across nanopores is fundamental to membrane separations, yet it remains poorly understood, especially for non-aqueous systems. Here, we design a chemically robust nanoporous graphene membrane and study molecular transport in various organic liquids under subnanometre confinement. We show that the nature of the solvent can modulate solute diffusion across graphene nanopores, and that breakdown of continuum flow occurs when pore size approaches the solvent's smallest molecular cross-section. By holistically engineering membrane support, modelling pore creation and defect management, high rejection and ultrafast organic solvent nanofiltration of dye molecules and separation of hexane isomers are achieved. The membranes exhibit stable fluxes across a range of solvents, consistent with flow across rigid pores whose size is independent of the solvent. These results demonstrate that nanoporous graphene is a rich materials system for controlling subcontinuum flow that could enable new membranes for a range of challenging separation needs.

Surface thermodynamics at the nanoscale

Fluid interfaces with nanoscale radii of curvature are generating great interest, both for their applications and as tools to probe our fundamental understanding. One important question is what is the smallest radius of curvature at which the three main thermodynamic combined equilibrium equations are valid: the Kelvin equation for the effect of curvature on vapor pressure, the Gibbs-Thomson equation for the curvature-induced freezing point depression, and the Ostwald-Freundlich equation for the curvature-induced increase in solubility. The objective of this Perspective is to provide conceptual, molecular modeling, and experimental support for the validity of these thermodynamic combined equilibrium equations down to the smallest interfacial radii of curvature. Important concepts underpinning thermodynamics, including ensemble averaging and Gibbs's treatment of bulk phase heterogeneities in the region of an interface, give reason to believe that these equations might be valid to smaller scales than was previously thought. There is significant molecular modeling and experimental support for all three of the Kelvin equation, the Gibbs-Thomson equation, and the Ostwald-Freundlich equation for interfacial radii of curvature from 1 to 4 nm. There is even evidence of sub-nanometer quantitative accuracy for the Kelvin equation and the Gibbs-Thomson equation.

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.

Diffusion of confined fluids in microporous zeolites and clay materials

Fluids exhibit remarkable variation in their structural and dynamic properties when they are confined at the nanoscopic scale. Various factors, including geometric restriction, the size and shape of the guest molecules, the topology of the host, and guest-host interactions, are responsible for the alterations in these properties. Due to their porous structures, aluminosilicates provide a suitable host system for studying the diffusion of sorbates in confinement. Zeolites and clays are two classes of the aluminosilicate family, comprising very ordered porous or layered structures. Zeolitic materials are important due to their high catalytic activity and molecular sieving properties. Guest molecules adsorbed by zeolites display many interesting features including unidimensional diffusion, non-isotropic rotation, preferred orientation and levitation effects, depending on the guest and host characteristics. These are useful for the separation of hydrocarbons which commonly exist as mixtures in nature. Similarly, clay materials have found application in catalysis, desalination, enhanced oil recovery, and isolation barriers used in radioactive waste disposal. It has been shown that the bonding interactions, level of hydration, interlayer spacing, and number of charge-balancing cations are the important factors that determine the nature of diffusion of water molecules in clays. Here, we present a review of the current status of the diffusion mechanisms of various adsorbed species in different microporous zeolites and clays, as investigated using quasielastic neutron scattering and classical molecular dynamics simulation techniques. It is impossible to write an exhaustive review of the subject matter, as it has been explored over several decades and involves many research topics. However, an effort is made to cover the relevant issues specific to the dynamics of different molecules in microporous zeolites and clay materials and to highlight a variety of interesting features that are important for both practical applications and fundamental aspects.

Kerogen nanoscale structure and CO2 adsorption in shale micropores

Gas storage and recovery processes in shales critically depend on nano-scale porosity and chemical composition, but information about the nanoscale pore geometry and connectivity of kerogen, insoluble organic shale matter, is largely unavailable. Using adsorption microcalorimetry, we show that once strong adsorption sites within nanoscale network are taken, gas adsorption even at very low pressure is governed by pore width rather than chemical composition. A combination of focused ion beam with scanning electron microscopy and transmission electron microscopy reveal the nanoscale structure of kerogen includes not only the ubiquitous amorphous phase but also highly graphitized sheets, fiber- and onion-like structures creating nanoscale voids accessible for gas sorption. Nanoscale structures bridge the current gap between molecular size and macropore scale in existing models for kerogen, thus allowing accurate prediction of gas sorption, storage and diffusion properties in shales.

Bridging scales in disordered porous media by mapping molecular dynamics onto intermittent Brownian motion

Owing to their complex morphology and surface, disordered nanoporous media possess a rich diffusion landscape leading to specific transport phenomena. The unique diffusion mechanisms in such solids stem from restricted pore relocation and ill-defined surface boundaries. While diffusion fundamentals in simple geometries are well-established, fluids in complex materials challenge existing frameworks. Here, we invoke the intermittent surface/pore diffusion formalism to map molecular dynamics onto random walk in disordered media. Our hierarchical strategy allows bridging microscopic/mesoscopic dynamics with parameters obtained from simple laws. The residence and relocation times - t_A, t_B - are shown to derive from pore size d and temperature-rescaled surface interaction ε/k_BT. t_A obeys a transition state theory with a barrier ~ε/k_BT and a prefactor ~10^-12 s corrected for pore diameter d. t_B scales with d which is rationalized through a cutoff in the relocation first passage distribution. This approach provides a formalism to predict any fluid diffusion in complex media using parameters available to simple experiments.

The role of the potential field on occurrence and flow of octane in quartz nanopores

Occurrence and flow of hydrocarbons in nanopores are two important issues in the effective exploitation of shale oil reservoirs. In this study, molecular dynamics simulations are employed to investigate the mechanisms about occurrence and flow of octane in slit-shaped quartz nanopores. We show that the occurrence state of octane and, therefore, its flow behavior are profoundly affected by the potential field from quartz walls and adsorption layers if the nanopore width w becomes less than 50 Å. Two main adsorption layers are always formed, adjacent to the walls and independent of w, due to two potential wells generated by the attractive potentials of the walls. Each pair of symmetrical adsorption layers, each of which can be considered as a solid-like surface, forms a confined environment similar to a nano-slit. The attractive potentials from them are found to be the cause for the formation of the adsorption layers between them. The obvious bulk phase of octane is formed in the pore of w = 50 Å due to the wide zero potential barrier induced by the innermost two adsorption layers. The nonlinear dependence of flow rate on pressure gradient shows that Darcy's law fails to describe the flow in the nanopore. The non-Darcy behavior mainly arises from adsorption effects from the walls and the adsorption layers, slippage between octane and walls and between adjacent two adsorption layers, and the molecular exchange between adsorption layers. A modified microscopic model is established to predict the dependence of flow rate on potential field, pressure gradient and w, which is in a good agreement with our simulation results and verified by the dodecane flow through the nanopore. Our work can be of great importance for revealing the mechanisms of occurrence and transport and guiding the estimation and exploitation of shale oil resources.

Tuning the selective permeability of polydisperse polymer networks

We study the permeability and selectivity ('permselectivity') of model membranes made of polydisperse polymer networks for molecular penetrant transport, using coarse-grained, implicit-solvent computer simulations. In our work, permeability P is determined on the linear-response level using the solution-diffusion model, P = KDin, i.e., by calculating the equilibrium penetrant partition ratio K and penetrant diffusivity Din inside the membrane. We vary two key parameters, namely the network-network interaction, which controls the degree of swelling and collapse of the network, and the network-penetrant interaction, which tunes the selective penetrant uptake and microscopic energy landscape for diffusive transport. We find that the partitioning K covers four orders of magnitude and is a non-monotonic function of the parameters, well interpreted by a second-order virial expansion of the free energy of transferring one penetrant from a reservoir into the membrane. Moreover, we find that the penetrant diffusivity Din in the polydisperse networks, in contrast to highly ordered membrane structures, exhibits relatively simple exponential decays. We propose a semi-empirical scaling law for the penetrant diffusion that describes the simulation data for a wide range of densities and interaction parameters. The resulting permeability P turns out to follow the qualitative behavior (including maximization and minimization) of partitioning. However, partitioning and diffusion are typically anti-correlated, yielding large quantitative cancellations, controlled and fine-tuned by the network density and interactions, as rationalized by our scaling laws. We finally demonstrate that even small changes of network-penetrant interactions, e.g., by half a kBT, modify the permselectivity by almost one order of magnitude.

Asphalt-related emissions are a major missing nontraditional source of secondary organic aerosol precursors

Asphalt-based materials are abundant and a major nontraditional source of reactive organic compounds in urban areas, but their emissions are essentially absent from inventories. At typical temperature and solar conditions simulating different life cycle stages (i.e., storage, paving, and use), common road and roofing asphalts produced complex mixtures of organic compounds, including hazardous pollutants. Chemically speciated emission factors using high-resolution mass spectrometry reveal considerable oxygen and reduced sulfur content and the predominance of aromatic (~30%) and intermediate/semivolatile organic compounds (~85%), which together produce high overall secondary organic aerosol (SOA) yields. Emissions rose markedly with moderate solar exposure (e.g., 300% for road asphalt) with greater SOA yields and sustained SOA production. On urban scales, annual estimates of asphalt-related SOA precursor emissions exceed those from motor vehicles and substantially increase existing estimates from noncombustion sources. Yet, their emissions and impacts will be concentrated during the hottest, sunniest periods with greater photochemical activity and SOA production.

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.

Mesoscopic method to study water flow in nanochannels with different wettability

Molecular dynamics (MD) simulations is currently the most popular and credible tool to model water flow in nanoscale where the conventional continuum equations break down due to the dominance of fluid-surface interactions. However, current MD simulations are computationally challenging for the water flow in complex tube geometries or a network of nanopores, e.g., membrane, shale matrix, and aquaporins. We present a novel mesoscopic lattice Boltzmann method (LBM) for capturing fluctuated density distribution and a nonparabolic velocity profile of water flow through nanochannels. We incorporated molecular interactions between water and the solid inner wall into LBM formulations. Details of the molecular interactions were translated into true and apparent slippage, which were both correlated to the surface wettability, e.g., contact angle. Our proposed LBM was tested against 47 published cases of water flow through infinite-length nanochannels made of different materials and dimensions-flow rates as high as seven orders of magnitude when compared with predictions of the classical no-slip Hagen-Poiseuille (HP) flow. Using the developed LBM model, we also studied water flow through finite-length nanochannels with tube entrance and exit effects. Results were found to be in good agreement with 44 published finite-length cases in the literature. The proposed LBM model is nearly as accurate as MD simulations for a nanochannel, while being computationally efficient enough to allow implications for much larger and more complex geometrical nanostructures.

Multicomponent Shale Oil Flow in Real Kerogen Structures via Molecular Dynamic Simulation

As an unconventional energy source, the development of shale oil plays a positive role in global energy, while shale oil is widespread in organic nanopores. Kerogen is the main organic matter component in shale and affects the flow behaviour in nanoscale-confined spaces. In this work, a molecular dynamic simulation was conducted to study the transport behaviour of shale oil within kerogen nanoslits. The segment fitting method was used to characterise the velocity and flow rate. The heterogeneous density distributions of shale oil and its different components were assessed, and the effects of different driving forces and temperatures on its flow behaviours were examined. Due to the scattering effect of the kerogen wall on high-speed fluid, the heavy components (asphaltene) increased in bulk phase regions, and the light components, such as methane, were concentrated in boundary layers. As the driving force increased, the velocity profile demonstrated plug flow in the bulk regions and a half-parabolic distribution in the boundary layers. Increasing the driving force facilitated the desorption of asphaltene on kerogen walls, but increasing the temperature had a negative impact on the flow velocity.

In Situ Determination of Carbon Number Distributions of Mixtures of Linear Hydrocarbons Confined within Porous Media Using Pulsed Field Gradient NMR

Pulsed field gradient (PFG) NMR measurements, combined with a novel optimization method, are used to determine the composition of hydrocarbon mixtures of linear alkanes (C7-C16) in both the bulk liquid state and when imbibed within a porous medium of mean pore diameter 28.6 nm. The method predicts the average carbon number of a given mixture to an accuracy of ±1 carbon number and the mole fraction of a mixture component to within an average root-mean-square error of ±0.036 with just three calibration mixtures. Given that the method can be applied at any conditions of temperature and pressure at which the PFG NMR measurements are made, the method has the potential for application in characterizing hydrocarbon liquid mixtures inside porous media and at the operating conditions relevant to, for example, hydrocarbon recovery and heterogeneous catalysis.

Nonempirical Free Volume Viscosity Model for Alkane Lubricants under Severe Pressures

Viscosities η and diffusion coefficients D_{s} of linear and branched alkanes at pressure 0<P<0.7  GPa and temperature T=500-600  K are calculated from molecular dynamics simulations. Combining Stokes-Einstein, free volume, and random walk concepts results in an accurate viscosity model for the considered P and T. All model parameters (hydrodynamic radius, random walk step size, and step frequency) are extracted from equilibrium molecular dynamics via microscopic ensemble averages rendering η(P,T) a parameter-free predictor for lubrication simulations.

Evidence of Facilitated Transport in Crowded Nanopores

Fluid transport in nature often occurs through crowded nanopores, where a number of phenomena can affect it, because of fluid-fluid and fluid-solid interactions, as well as the presence of organic compounds filling the pores and their structural fluctuations. Employing molecular dynamics, we probe here the transport of fluid mixtures (CO₂-CH₄ and H₂S-CH₄) through silica nanopores filled with benzene. Both CO₂ and H₂S are strongly adsorbed within the organic-filled pore, partially displacing benzene. Unexpectedly, CO₂/H₂S adsorption facilitates CH₄ transport. Analysis of the trajectories suggests that both CO₂ and H₂S act as vehicle-like carriers and might swell benzene, generating preferential transport pathways within the crowded pore. The results are useful for identifying unexpected transport mechanisms and for developing engineering approaches that could lead to storage of CO₂ in caprocks.

The Imaging Resolution and Knudsen Effect on the Mass Transport of Shale Gas Assisted by Multi-length Scale X-Ray Computed Tomography

The spatial resolution of 3D imaging techniques is often balanced by the achievable field of view. Since pore size in shales spans more than two orders of magnitude, a compromise between representativeness and accuracy of the 3D reconstructed shale microstructure is needed. In this study, we characterise the effect of imaging resolution on the microstructural and mass transport characteristics of shales using micro and nano-computed tomography. 3D mass transport simulation using continuum and numerical physics respectively is also compared to highlight the significance of the Knudsen effect on the reconstructed solid surface. The result shows that porosity measured by micro-CT is 25% lower than nano-CT, resulting in an overestimated pore size distribution and underestimated pore connectivity. This leads to a higher simulated intrinsic permeability. An overestimated diffusive flux and underestimated permeability are obtained from the continuum mass transport simulation compared to the numerical ones when the molecular-wall collision is accounted, evidenced by the large deviation of the measured Knudsen tortuosity factor and permeability correction factor. This study is believed to provide new knowledge in understanding the importance of imaging resolution and gas flow physics on mass transport in porous media.

Distribution and Mobility of Crude Oil-Brine in Clay Mesopores: Insights from Molecular Dynamics Simulations

The value of crude oil accommodated in shale has been recognized and has attracted increasing attention from the academic and industrial society. The occurrence and mobility of crude oil in clay pores, therefore, become essential issues for evaluation and recovery of shale oil. The distribution, structure, and transport of the oil-brine mixture confined in a slit-shaped montmorillonite mesopore with different water amounts have been investigated using equilibrium molecular dynamics and nonequilibrium molecular dynamics (NEMD) simulations. A mimic model of crude oil, a mixture of 19 organic molecules, was employed, and thus the behavior of different organic molecules could be characterized in detail. A temperature of 410 K and a pressure of 300 atm corresponding to a buried depth of 3 km were employed. The simulations indicate that the water amount determines the distribution of crude oil. Water and metal ions prefer to cover on hydrophilic montmorillonite surfaces, while nonpolar hydrocarbons tend to be far away from clay surfaces. As the water amount is too low to completely cover the clay surfaces, some polar organic molecules will come into contact with the uncovered clay surface. Abundant organic acid molecules adsorb onto montmorillonite surfaces mainly through participating in the inner-sphere complexes of Na⁺ ions closely located at montmorillonite surfaces (i.e., Na⁺ cation bridge) and forming hydrogen bonds with water molecules in the vicinity. Carbazole molecules tend to aggregate together due to π-π stacking, while thioether molecules mix within alkane molecules and exhibit no characteristic distributions. The mobility of all oil components decreases with the decrease of the water amount, and the mobility of polar components (i.e., organic acid and carbazole) is relatively lower than that of nonpolar hydrocarbons. NEMD simulations clearly indicate that the transport velocity of crude oil markedly increases with the water amount under a specific pressure gradient. The brine covering on clay surfaces significantly weakens oil-clay interfacial interactions. Polar components, especially organic acid, exhibit relatively low transport velocity compared with nonpolar hydrocarbons. These findings highlight the understanding of physical-chemical behaviors of shale oil and provide atomistic information for technology development for enhancing oil recovery.

Adsorption and Capillary Condensation-Induced Imbibition in Nanoporous Media

Multiphase flow phenomena in nanoporous media are encountered in many science and engineering applications. Shales, for example, possessing complex nanopore networks, have considerable importance as source rocks for unconventional oil and gas production and as low-permeability seals for geologic carbon sequestration or nuclear waste disposal. This study presents a theoretical investigation of the processes controlling adsorption, capillary condensation, and imbibition in such nanoporous media, with a particular focus on understanding the effects of fluid-fluid and fluid-pore wall interaction forces in the interconnected nanopore space. Building on a new theoretical framework, we developed a numerical model for the multiphase nanoporous flow and tested it against water vapor uptake measurements conducted on a shale core sample. The model, which is based on the density functional approach, explicitly includes the relevant interaction forces among fluids and solids while allowing for a continuum representation of the porous medium. The experimental data include gravimetrically measured mass changes in an initially dry core sample exposed to varying levels of relative humidity, starting with a low relative humidity (rh = 0.31) followed by a period of a higher relative humidity (rh = 0.81). During this process, water vapor uptake in the dry core is recorded as a function of time. Our model suggests that, under low rh conditions, the flow within the shale sample is controlled by adsorption- and diffusion-type processes. After increasing the rh to 0.81, the uptake of water vapor becomes more significant, and according to our model, this can be explained by capillary condensation followed by immiscible displacement in the core sample. It appears that strong fluid-pore wall attractive forces cause condensation near the inlet, which then induces water imbibition further into sample.

Methane Diffusion in a Flexible Kerogen Matrix

It has been recognized that the microporosity of shale organic matter, especially that of kerogen, strongly affects the hydrocarbon recovery process from unconventional reservoirs. So far, the numerical studies on hydrocarbon transport through the microporous phase of kerogen have neglected the effect of poromechanics, that is, the adsorption-induced deformations, by considering kerogen as a frozen, nondeformable, matrix. Here, we use molecular dynamics simulations to investigate methane diffusion in an immature (i.e., with high H/C ratio) kerogen matrix, while explicitly accounting for adsorption-induced swelling and internal matricial motions, covering both phonons and nonperiodic internal deformations. However, in the usual frozen matrix approximation, diffusivity decreases with increasing fluid loading, as evidenced by a loss of free volume, accounting for adsorption-induced swelling that gives rise to an increase in free volume and, hence, in diffusivity. The obtained trend is further rationalized using a Fujita-Kishimoto free volume theory initially developed in the context of diffusion in swelling polymers. We also quantify the enhancing effect of the matrix internal motions (i.e., at fixed volume) and show that it roughly gives an order of magnitude increase in diffusivity with respect to a frozen matrix, thanks to fluctuations in the pore connectivity. We eventually discuss the possible implications of this work to explain the productivity slowdown of hydrocarbon recovery from shale immature reservoirs.

The Constructions and Pyrolysis of 3D Kerogen Macromolecular Models: Experiments and Simulations

Kerogens are extracted from deep shales to study pyrolysis of deep shale samples. The 2D molecular models of kerogens are obtained by a series of physical and chemical experiments by which the macromolecular models of kerogens are constructed. Then, the reasonable 3D macromolecular models are established by molecular mechanics and global energy minimization. The effects of temperature and heating rate on the chemical kinetics of kerogen pyrolysis are studied using reactive force field (ReaxFF). The hybrid molecular dynamics/force-biased Monte Carlo (MD/fbMC) approach is used to simulate the pyrolytic process at the experimental temperature, which is lower than the conventional one. The gaseous products and residues obtained by the simulations agree with the experimental results, which means a reliable simulation method for pyrolysis at experimental temperature is provided. This study constructs the rational macromolecular models of kerogen by experiments, and proposes the mechanisms of typical reactions of kerogen pyrolysis, which may help in understanding the formation of shale oil and gas.