Nonequilibrium molecular dynamics simulation of diffusion and flow in thin microporous membranes

Shale Gas Nanofluid in the Curved Carbon Nanotube: A Molecular Dynamics Simulation Study

Curved nanochannels are prevalent in porous and tortuous materials, with shale matrices being a noteworthy example. The tortuosity of shale matrices significantly influences the behavior of shale gas, holding crucial implications for gas recovery engineering. In this study, we employ molecular dynamics simulation (MD) to investigate the impact of curvature and radius in tortuous nanochannel formed by a curved single-walled carbon nanotube (SWCNT) on the adsorption and transport properties of methane gas fluid. Our findings reveal that the inner half surface of the SWCNT, characterized by negative curvature, exhibits enhanced methane adsorption. Methane in straighter and narrower channels displays higher flow velocities, while wider channels exhibit higher flow flux. The nonzero flow velocity alters adsorption strength, causing the outer half to surpass the inner half. Tangent and vertical velocities of the flow are heterogeneously distributed in the channel, with the outer half having higher tangent velocities. Additionally, a vertical velocity pulse near the entrance induces turbulent vortex flow, slowing down the tangent flow velocity. This research contributes to a deeper understanding of shale gas properties in matrices with bent and curved channels, offering insights into nanofluids in carbon nanotubes and porous media featuring curved nanochannels.

Effects of π-π Stacking on Shale Gas Adsorption and Transport in Nanopores

The π-π interaction is a prevalent driving force in the formation of various organic porous media, including the shale matrix. The configuration of π-π stacking in the shale matrix significantly influences the properties of shale gas and plays a crucial role in understanding and exploiting gas resources. In this research, we investigate the impact of different π-π stacking configurations on the adsorption and transport of shale gas within the nanopores of the shale matrix. To achieve this, we construct kerogen nanopores using π-π stacked columns with varying stacking configurations, such as offset/parallel stacking types and different orientations of the stacked columns. Through molecular dynamics simulations, we examined the adsorption and transport of methane within these nanopores. Our findings reveal that methane exhibits stronger adsorption in smoother nanopores, with this adsorption remaining unaffected by the nanoflow. We observe a heterogeneous distribution of the 2D adsorption free energy, which correlates with the specific π-π stacking configurations. Additionally, we introduce the concept of "directional roughness" to describe the surface characteristics, finding that the nanoflow flux increases as the roughness decreases. This research contributes to the understanding of shale gas behavior in the shale matrix and provides insights into nanoflow properties in other porous materials containing π-π stackings.

Mass Transfer through Vapor-Liquid Interfaces Studied by Non-Stationary Molecular Dynamics Simulations

Molecular dynamics (MD) simulations are highly attractive for studying the influence of interfacial effects, such as the enrichment of components, on the mass transfer through the interface. In a recent work, we have presented a steady-state MD simulation method for investigating this phenomenon and tested it using model mixtures with and without interfacial enrichment. The present study extends this work by introducing a non-stationary MD simulation method. A rectangular simulation box that contains a mixture of two components 1 + 2 with a vapor phase in the middle and two liquid phases on both sides is used. Starting from a vapor-liquid equilibrium state, a non-stationary molar flux of component 2 is induced by inserting particles of component 2 into the center of the vapor phase in a pulse-like manner. During the isothermal relaxation process, particles of component 2 pass through the vapor phase, cross the vapor-liquid interface, and enter the liquid phase. The system thereby relaxes into a new vapor-liquid equilibrium state. During the relaxation process, spatially resolved responses for the component densities, fluxes, and pressure are sampled. To reduce the noise and provide measures for the uncertainty of the observables, a set of replicas of simulations is carried out. The new simulation method was applied to study mass transfer in two binary Lennard-Jones mixtures: one that exhibits a strong enrichment of the low-boiling component 2 at the vapor-liquid interface and one that shows no enrichment. Even though both mixtures have similar transport coefficients in the bulk phases, the results for mass transfer differ significantly, indicating that the interfacial enrichment influences the mass transfer.

Nonequilibrium Steady States in Fluid Transport through Mesopores: Dynamic Mean Field Theory and Nonequilibrium Molecular Dynamics

We present a dynamic mean field theory (DMFT) and nonequilibrium dual control volume grand canonical molecular dynamics (GCMD) simulation study of steady-state fluid transport in slit-shaped mesopores under an applied chemical potential gradient. The main focus is on states where the bulk conditions on one side of the pore would lead to a capillary condensed state in the pore at equilibrium while those on the other side would lead to a vapor state in the pore. This choice of conditions is motivated by certain separation applications in which condensable vapors permeate through mesoporous membranes. Under these circumstances, we have found partially filled states with a liquid-like state at the high chemical potential end of the pore and a vapor-like state at the low chemical potential end. This phenomenon is accompanied by hysteresis. The existence of partially filled states has been hypothesized in previous work but the present paper reveals them as an emergent feature of the systems. We find that predictions of DMFT are in good qualitative agreement with the overall GCMD results. However, the GCMD results demonstrate that the transport is faster through the partially filled pore than through the unfilled pore, a feature not captured by DMFT.

A comparison of dynamic mean field theory and grand canonical molecular dynamics for the dynamics of pore filling and capillary condensation of fluids in mesopores

We use results from grand canonical molecular dynamics (GCMD) to test the predictions from dynamic mean field theory (DMFT) for the pore filling and capillary condensation mechanisms of a fluid confined in slit shaped mesopores. The theory predicts that capillary condensation occurs by a nucleation process in which a liquid bridge forms between the two walls, and the pore is filled via the growth of this bridge. For longer pores, multiple bridging is seen. These mechanisms are confirmed by the molecular dynamics simulations. The primary difference between the theory and simulations lies in the role of fluctuations. DMFT predicts a single nucleation time and location, while in GCMD (and in nature) a distribution of nucleation times and locations is seen.

Computational study of pressure-driven methane transport in hierarchical nanostructured porous carbons

Using the reflecting particle method together with a perturbation-relaxation loop developed in our previous work, we studied pressure-driven methane transport in hierarchical nanostructured porous carbons (HNPCs) containing both mesopores and micropores in non-equilibrium molecular dynamics simulations. The surface morphology of the mesopore wall was systematically varied by tuning interaction strength between carbon atoms and the template in a mimetic nanocasting process. Effects of temperature and mesopore size on methane transport in HNPCs were also studied. Our study shows that increased mesopore wall surface roughness changes the character of the gas-wall interaction from specular to diffuse, while the gas-gas interaction is diminished due to the decrease of adsorption density. Effects of the mesopore wall surface morphology are the most significant at low temperatures and in small channels. Our systematic study provides a better understanding of the transport mechanisms of light gases through carbon nanotube composite membranes in experiments.

Computational Study of Pressure-Driven Gas Transport in Nanostructured Carbons: An Alternative Approach

We demonstrated a computationally efficient method in nonequilibrium molecular dynamics (NEMD) simulations to study pressure-driven gas transport in porous media. The reflecting particle method (RPM)14 was used to establish a steady-state gas flow along the transport channel, and the gas density in the feed chamber was properly adjusted to allow a constant pressure drop under various conditions by using a perturbation-relaxation loop developed here. This method was validated for methane flow through carbon nanotubes over a wide range of temperatures, giving results comparable to those of the commonly used dual control volume grand canonical molecular dynamics (DCV-GCMD) method but at least 20 times more efficient, even though the transport condition tested is favorable for the latter. This made it possible to perform systematic studies on the effects of temperature, pressure, and channel size on the transport behaviors. Our study shows that adsorption density varies significantly with temperature, which dramatically influences the transport mechanisms, especially in small channels at low temperatures and under high pressures. This newly developed NEMD method can be readily extended to study gas transport through channels with more complex surface morphology.

Bottom-up model of adsorption and transport in multiscale porous media

We develop a model of transport in multiscale porous media which accounts for adsorption in the different porosity scales. This model employs statistical mechanics to upscale molecular simulation and describe adsorption and transport at larger time and length scales. Using atom-scale simulations, which capture the changes in adsorption and transport with temperature, pressure, pore size, etc., this approach does not assume any adsorption or flow type. Moreover, by relating the local chemical potential μ(r) and density ρ(r), the present model accounts for adsorption effects and possible changes in the confined fluid state upon transport. This model constitutes a bottom-up framework of adsorption and transport in multiscale materials as it (1) describes the adsorption-transport interplay, (2) accounts for the hydrodynamics breakdown at the nm scale, and (3) is multiscale.

Molecular simulations of supercritical fluid permeation through disordered microporous carbons

Fluid transport through microporous carbon-based materials is inherent in numerous applications, ranging from gas separation by carbon molecular sieves to natural gas production from coal seams and gas shales. The present study investigates the steady-state permeation of supercritical methane in response to a constant cross-membrane pressure drop. We performed dual control volume grand canonical molecular dynamics (DCV-GCMD) simulations to mimic the conditions of actual permeation experiments. To overcome arbitrary assumptions regarding the investigated porous structures, the membranes were modeled after the CS1000a and CS1000 molecular models, which are representative of real microporous carbon materials. When adsorption-induced molecular trapping (AIMT) mechanisms are negligible, we show that the permeability of the microporous material, although not significantly sensitive to the pressure gradient, monotonically decreases with temperature and reservoir pressures, consistent with diffusion theory. However, when AIMT occurs, the permeability increases with temperature in agreement with experimental data found in the literature.

Slippage and viscosity predictions in carbon micropores and their influence on CO2 and CH4 transport

Non-equilibrium molecular dynamics simulations of pure carbon dioxide and methane and their equimolar mixtures have been carried out with an external driving force imposed on carbon slit pores to investigate gas slippage and Klinkenberg effects. Simulations were conducted to determine the effect of pore size and exposure to an external potential on the velocity profile and slip-stick boundary conditions. The simulations indicate that molecule-wall collisions influence the velocity profile, which deviates significantly from the Navier-Stokes hydrodynamic prediction for micro- and mesopores. Also, the shape of the velocity profile is found to be independent of the applied pressure gradient in micropores. The results indicate that the velocity profile is uniform for pore sizes less than 2 nm (micropores) where the transport is mainly due to molecular streaming or Knudsen diffusion and, to a lesser extent, molecular diffusion. As pore sizes increase to 10 nm, parabolic profiles are observed due to the reduced interaction of gas molecules with the pore walls. A 3D pore network, representative of porous carbon-based materials, has been generated atomistically using the Voronoi tessellation method. Simulations have been carried out to determine the effect of the pore structure and modeled viscosity on permeability and Klinkenberg parameters. The use of the bulk-phase viscosity for estimating the permeability of CO(2) in units of Darcy in a 3D micropore network is not an appropriate assumption as it significantly underestimates the CO(2) permeability. On the other hand, since the transport properties of CH(4) are less influenced by the pore walls compared with CO(2), the use of the bulk-phase CH(4) viscosity estimates are a reasonable assumption.

On the cavitation and pore blocking in slit-shaped ink-bottle pores

We present GCMC simulations of argon adsorption in slit pores of different channel geometry. We show that the isotherm for an ink-bottle pore can be reconstructed as a linear combination of the local isotherms of appropriately chosen independent unit cells. Second, depending on the system parameters and operating conditions, the phenomena of cavitation and pore blocking can occur for a given configuration of the ink-bottle pore by varying the geometrical aspect ratio. Although it has been argued in the literature that the geometrical aspects of the system govern the evaporation mechanism (either cavitation or pore blocking), we here put forward an argument that the local compressibility in different parts of the ink-bottle pore is the deciding factor for evaporation. When the fluid in the small neck is strongly bound, cavitation is the governing process, and molecules in the cavity evaporate to the surrounding bulk gas via a mass transfer mechanism through the pore neck. When the pore neck is sufficiently large, the system of neck and cavity evaporates at the same pressure, which is a consequence of the comparable compressibility between the fluid in the neck and that in the cavity. This suggests that local compressibility is the measure of cohesiveness of the fluid prior to evaporation. One consequence that we derive from the analysis of isotherms of a number of connected pores is that by analyzing the adsorption branch or the desorption branch of an experimental isotherm may not lead to the correct pore sizes and the correct pore volume distribution.

Massively Parallel Molecular Dynamics Simulation of Gas Permeation across Molecular Sieving Porous Membranes

In this work we simulate the diffusion of gases in a microporous solid models using a newly developed dual control volume grand canonical molecular dynamics technique. This allows spatial variation of chemical potential and hence an accurate simulation of steady-state pressure driven diffusion. The molecular sieving nature of microporous zeolites are discussed and compared with that for amorphous silica from sol-gel methods. Massively parallel supercomputers allow a quick and insightful study of these microporous structures.

Colloidal permeability of liquid membranes consisting of hard particles by nonequilibrium simulations

A novel particulate membrane, comprised of a confined fluid of colloidal hard spheres, is presented and studied by means of simulations. Using a fluid of smaller hard spheres as feed, the transport properties of the membrane are studied as a function of the volume fractions of both the feed solution and membrane and the size ratio between both types of particles. Our simulations show that the fluid in the membrane is compressed to the permeate side due to the pressure of the feed. This effect controls the permeability behavior of the membrane: impermeable when the feed pressure is too low, or when the pressure is high enough to induce crystallization of the membrane fluid. Thus, the permeability first increases and then decreases, upon increasing the feed concentration. Finally we focus in systems with high concentrations of the feed and membrane fluids, where completely impermeable membranes are obtained only when the feed spheres are big enough (sigma(f)>0.38sigma(m)).

Temperature control algorithms in dual control volume grand canonical molecular dynamics simulations of hydrogen diffusion in palladium

The effectiveness of five temperature control algorithms for dual control volume grand canonical molecular dynamics is investigated in the study of hydrogen atom diffusion in a palladium bulk. The five algorithms, namely, Gaussian, generalized Gaussian moment thermostat (GGMT), velocity scaling, Nosé-Hoover (NH), and its enhanced version Nosé-Hoover chain (NHC) are examined in both equilibrium and nonequilibrium simulation studies. Our numerical results show that Gaussian yields the most inaccurate solutions for the hydrogen-palladium system due to the high friction coefficient generated from the large velocity fluctuation of hydrogen, while NHC, NH, and GGMT produce the most accurate temperature and density profiles in both equilibrium and nonequilibrium cases with their feedback control mechanisms. However, this feedback control also overestimates the self-diffusion coefficients in equilibrium systems and the diffusion coefficient in nonequilibrium systems. Velocity scaling thermostat produces slight inhomogeneities in the temperature and density profiles, but due to the dissipated heat accumulated in the control volumes it still yields accurate self-diffusion coefficients that are in good agreement with the experimental data at a wide range of temperatures while others tend to deviate.

Computer simulation of adsorption kinetics of surfactants on solid surfaces

Adsorption kinetics of surfactants on solid surfaces has been studied by using computer simulation. Both bulk surfactant concentration and diffusion region are explicitly integrated in our model. Depending on the head-surface interaction, our simulation results indicate that there exist two different kinetic modes in adsorption process of surfactants on solid surfaces. One is the four-regime mode and the other is step-wise mode. For the strongly attractive head-surface interaction, four distinct regimes of surfactant adsorption are found: a diffusion-controlled regime, a self-assembly controlled regime, an intermediate coverage regime and a saturated regime. In particular, the adsorption in second regime displays a power-law time dependence with an exponent unrelated to bulk concentrations and diffusion coefficients. While for the weaker adsorption surfaces, the step-wise mode is found. The mode includes a low-coverage nucleation regime and the saturated regime after a sudden aggregation of surfactants on the substrates which occurs stochastically. Besides the head-surface interaction, in this work, the effects of surfactant diffusivity, bulk concentration, the length of diffusion zone and surfactant architecture on the adsorption kinetics are also considered. The simulated adsorption kinetics is compared qualitatively with experimental results.

Molecular simulation of pressure-driven fluid flow in nanoporous membranes

An extended nonequilibrium molecular dynamics technique has been developed to investigate the transport properties of pressure-driven fluid flow in thin nanoporous membranes. Our simulation technique allows the simulation of the pressure-driven permeation of liquids through membranes while keeping a constant driving pressure using fluctuating walls. The flow of argon in the liquid state was simulated on applying an external pressure difference of 2.4x10(6) Pa through the slitlike and cylindrical pores. The volume flux and velocity distribution in the membrane pores were examined as a function of pore size, along with the interaction with the pore walls, and these were compared with values estimated using the Hagen-Poiseuille flow. The calculated velocity strongly depends on the strength of the interaction between the fluid and the atoms in the wall when the pore size is approximately<20sigma. The calculated volume flux also shows a dependence on the interaction between the fluid and the atoms in the wall. The Hagen-Poiseuille law overestimates or underestimates the flux depending on the interaction. From the analysis of calculated results, a good linear correlation between the density of the fluid in the membrane pores and the deviation of the flux estimated from the Hagen-Poiseuille flow was found. This suggests that the flux deviation in nanopore from the Hagen-Poiseuille flow can be predicted based on the fluid density in the pores.

Molecular dynamics simulation of a pressure-driven liquid transport process in a cylindrical nanopore using two self-adjusting plates

Fluid transport through a nanopore in a membrane was investigated by using a novel molecular dynamics approach proposed in this study. The advantages of this method, relative to dual-control-volume grand-canonical molecular dynamics method, are that it eliminates disruptions to the system dynamics that are normally created by inserting or deleting particles from control volumes, and that it functions well for dense systems due to the number of particles being fixed in the system. Using the proposed method, we examined liquid argon transport through a nanopore by performing nonequilibrium molecular dynamics (NEMD) simulations under different back pressures. Validation of the code was performed by comparing simulation results to published experimental data obtained under equilibrium conditions. NEMD results show that constant pressure difference across the membrane was readily achieved.

Kinetic Coefficients for Mixed Adsorbate Fluids in Narrow Pores

The kinetic coefficients (trace diffusion, mutual diffusion and shear viscosity) of molecules in slit-like and sphero-cylindrical mesoporous systems were studied in terms of the modified lattice-gas model (LGM). The LGM equations were derived for molecules of the mixture having a spherical shape and similar size. A new equation for the velocity of the thermal molecule was used. The theory takes the change in the mechanism of particle migration in different phases into account, viz. from pair collisions for the gas to the overcoming of the activation barrier by thermofluctuation for dense phases. At low mixture densities corresponding to an ideal gas phase, the LGM expression for the mutual diffusion coefficient agrees with the expression of the rigorous kinetic theory of gases. The theory allows the calculation of the kinetic coefficients for the components of binary mixtures in full gas-liquid density areas. The supramolecular structure of the sphero-cylindrical system was modelled by sections with a simple regular geometry (cylindrical and spherical) with the additional inclusion of junctions between different pore sections. The contributions of the near-wall regions caused by the molecule-wall potential to the general appearance of the phase diagrams and the effect of the pore size on the capillary condensation conditions were discussed.