Volume Grand Canonical Molecular Dynamics Research Articles

Modeling competitive adsorption and diffusion of CH4/CO2 mixtures confined in mature type-II kerogen: Insights from molecular dynamics simulations

In this study, the adsorption and competitive diffusion of methane (CH4) and carbon dioxide (CO2) mixtures through a molecular model of mature type-2 kerogen was investigated using molecular dynamics simulations. The Dual Control Volume-Grand Canonical Molecular Dynamics method was used to analyze the system and the results were focused on the selectivity of kerogen towards mixtures under a wide range of thermodynamic conditions. The results showed that the adsorption selectivity of CO2/CH4 was around 2–4 and decreased with temperature in the range 350–450 K. The Extended Langmuir (EL) model was found to underestimate the selectivity, and a correction was proposed in the form of the Corrected Extended Langmuir (CEL) model, which improved the estimations of the adsorption of CH4/CO2 mixtures in kerogen with only one adjustable parameter independent of thermodynamic conditions. Interestingly, we noticed that, out of equilibrium, the adsorption selectivity was not affected by the flow conditions when a pressure gradient was imposed, and the CEL model can thus be used to describe the contribution of adsorption to the selectivity under flow conditions. The results showed that the ratio of the collective diffusion coefficients of CH4 and CO2 was around 0.3−0.4, which was about two times lower than other simulations found in the literature. To describe the global selectivity, a simple approach combining the CEL model and the average ratio of diffusion coefficients was proposed, resulting in a selectivity of around 1.

A permeation model of shale gas in cylindrical-like kerogen pores at geological conditions

Understanding the diffusion and permeation behavior of shale gas at geological depths is significantly important to exploration of shale gas, while the permeation mechanism of shale gas in shale gas reservoir is closely related to the confined fluid behavior at mesoscopic scale and cannot be described by traditional Fick or Knudsen diffusion models. In this work, we use the dual control volume grand canonical molecular dynamics method to systematically investigate the permeation processes of shale gas in cylindrical -like kerogen pores represented by the carbon nanotube at different geological depths, and hundreds of simulation data in different pressures, temperatures and pore diameter are obtained. By analyzing these simulated data, we propose a new permeation model to describe the permeability of shale gas in cylindrical-like kerogen pores at geological depths. The new model can satisfactorily reproduce the extrapolation testing data of permeability of shale gas, and perfectly bridge the gap between macroscopic Fick model and microscopic Knudsen model, which provides a useful guidance and reference for exploration of shale gas.

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.

Molecular Simulations of Binary Gas Mixture Transport and Separation in Slit Nanopores

We propose a new method to simulate the gas mixture transport and separation in slit nanopores. The method is based on the random removal of molecules from the permeate side in the dual control volume–grand canonical molecular dynamics (DCV-GCMD) method. Each step in the random removal is independent of the previous steps. The conventional method, DCV-GCMD, simulates the gas mixture in control volumes based on the chemical potential of each component, in which the gas compositions have to be known in advance and kept constant. However, the transport process affects the composition of the produced gas mixture due to selective adsorption in the nanopores. This process has been modeled iteratively in the literature. We propose an alternative method to calculate the composition in the permeate side directly; in our approach, the computational efficiency is improved by an order of magnitude compared to the iterative method. Transport of gas mixtures of CH4/He and CO2/CH4 is investigated in graphene, graphite, and tetrahedral–octahedral–tetrahedral (TOT) structure slit pores. Pore width is the dominant factor in the species separation. The solid substrates and surface roughness have a pronounced effect on gas separation. The average pressure may have a pronounced effect when the pore width is less than 1.00 nm.

Fluid-fluid interfacial mobility from random walks

Dual control volume grand canonical molecular dynamics is used to perform the first calculation of fluid-fluid interfacial mobilities. The mobility is calculated from one-dimensional random walks of the interface by relating the diffusion coefficient to the interfacial mobility. Three different calculation methods are employed: one using the interfacial position variance as a function of time, one using the mean-squared interfacial displacement, and one using the time-autocorrelation of the interfacial velocity. The mobility is calculated for two liquid-liquid interfaces and one liquid-vapor interface to examine the robustness of the methods. Excellent agreement between the three calculation methods is shown for all the three interfaces, indicating that any of them could be used to calculate the interfacial mobility.

A mesoscale model for diffusion and permeation of shale gas at geological depth

The demand on energy is rising and shale gas as an important unconventional energy resource has received worldwide attention. It has shown a significant effect on the world's energy structure after the commercial exploitation of shale gas in the United States. Understanding diffusion and permeation of shale gas at geological depths is quite essential, but it cannot be described by traditional Fick or Knudsen diffusion models. In this work, we use dual control volume–grand canonical molecular dynamics method to systematically investigate the permeation process of shale gas in montmorillonite (i.e., a clay mineral of shale) at different geological depths. Results indicate that temperature, pressure, and pore size have an important effect on the permeability, and Knudsen equation cannot describe the permeability of shale gas. Accordingly, on the basis of these simulated data, we propose a new mesoscale model to describe the permeability of shale gas at geological depths. The new mesoscale model shows extensive applicability and can excellently reproduce the extrapolation testing data, and it satisfactorily bridges the gap between Knudsen diffusion and Fick diffusion, which provides important fundamentals for exploitation of shale gas. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1059–1066, 2018

Effect of nano-confinement on high pressure methane flow characteristics

High pressure gas flow in shale nanoporous media plays an important role in shale gas recovery. The objective of this work is to study the effect of confinement on high pressure methane flow in nanoscale pores. We used dual control volume grand canonical molecular dynamics for different temperatures and pore sizes and compared our results with conventional hydrodynamic equation. We observed that when pore size is larger than 2 nm, flux increases with pore size. But when pore size is less than 2 nm, flux shows varying behaviors depending on the pore size due to methane molecular configurations and structures under different nano-confinements. We also observed that enhancement over the prediction from Hagen-Poiseuille equation can be more than two orders of magnitude in nanopores of around 1 nm pore size. Similar to previous computer simulation and experiments on liquid flow in nanopores, the dependences of the enhancement factor ε and the calculated slip length Ls on the pore sizes show discontinuity within three distinct regions: R1) pore size less than 0.8 nm; R2) between 0.8 and 1.0 nm; and R3) larger than 1.0 nm. Within R2 and R3, ε and Ls monotonically decrease with pore size. The methane molecular flux, enhancement factor, and calculated slip length increase from 328.15 K to 368.15 K, but remain comparable for 368.15 K and 408.15 K.

Flow of Gases in Organic Nanoscale Channels: A Boundary-Driven Molecular Simulation Study

In modeling fluid transport in organic nanopores of shale, particular attention should be paid to the gas–wall interactions, specifically the adsorption phenomena, and the fact that the size of pores are comparable with the mean-free-path of the gas molecules. The objective for this work is to investigate the significance of the adsorbed gas molecules in the total mass flux of organic nanoscale channels. Molecular dynamics (MD) has proven to be a credible technique to examine dynamics of atomic-level phenomena. In this study, transport of four different gases, methane and argon (high adsorption affinity) and helium and neon (low adsorption affinity), is studied, and their velocity and mass flux profiles are analyzed using dual control volume grand canonical molecular dynamics (DCV-GCMD) simulations. DCV-GCMD simulations are performed for different pressures, pressure gradients, and channel sizes. Computed normalized velocities are close to 1 for all the gases and channel heights, which shows that the velo...

Phase behavior and flow in shale nanopores from molecular simulations

Phase behavior and flow in shale nanopores, due to fluid heterogeneity, cannot be described by bulk and continuum-based formulations. The interactions between fluid and rock molecules are important in both phase behavior and flow. As a result, frameworks from bulk equations of state in phase behavior, and continuum mechanisms and Klinkenberg slippage in flow may become inapplicable. Recently, we have studied both phase behavior and flow in nanopores using density functional theory and various molecular simulations. This work addresses a number of issues related to the adsorption of mixtures of hydrocarbons, carbon dioxide and water as well as methane flow at different pressure conditions in nanopores. For flow, we use the dual control volume-grand canonical molecular dynamics (DCV-GCMD) simulation as in our previous work. We use a smaller pressure difference between high and low pressure reservoirs connected to the nanopores. We find that similar to our past work, the flux of methane in the slit pores can be two orders of magnitude higher than the results from the Hagen-Poiseuille equation.

Flow of methane in shale nanopores at low and high pressure by molecular dynamics simulations.

Flow in shale nanopores may be vastly different from that in the conventional permeable media. In large pores and fractures, flow is governed by viscosity and pressure-driven. Convection describes the process. Pores in some shale media are in nanometer range. At this scale, continuum flow mechanism may not apply. Knudsen diffusion and hydrodynamic expressions such as the Hagen-Poiseuille equation and their modifications have been used to compute flow in nanopores. Both approaches may have drawbacks and can significantly underestimate molecular flux in nanopores. In this work, we use the dual control volume-grand canonical molecular dynamics simulations to investigate methane flow in carbon nanopores at low and high pressure conditions. Our simulations reveal that methane flow in a slit pore width of 1-4 nm can be more than one order of magnitude greater than that from Knudsen diffusion at low pressure and the Hagen-Poiseuille equation at high pressure. Knudsen diffusion and Hagen-Poiseuille equations do not account for surface adsorption and mobility of the adsorbed molecules, and inhomogeneous fluid density distributions. Mobility of molecules in the adsorbed layers significantly increases molecular flux. Molecular velocity profiles in nanopores deviate significantly from the Navier-Stokes hydrodynamic predictions. Our molecular simulation results are in agreement with the enhanced flow measurements in carbon nanotubes.

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.

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.

Relation Between Flow Enhancement Factor and Structure for Core-Softened Fluids Inside Nanotubes

The relationship between enhancement flow and structure of core-softened fluids confined inside nanotubes has been studied using nonequilibrium molecular dynamics simulation. The fluid was modeled with different types of attractive and purely repulsive two length scale potentials. Such potentials reproduce in bulk the anomalous behavior observed for liquid water. The dual control volume grand canonical molecular dynamics method was employed to create a pressure gradient between two reservoirs connected by a nanotube. We show how the nanotube radius affects the flow enhancement factor for each one of the interaction potentials. The connection between structural and dynamical properties of the confined fluid is discussed, and we show how attractive and purely repulsive fluids exhibit distinct behaviors. A continuum to subcontinuum flow transition was found for small nanotube radius. The behavior obtained for the core-softened fluids is similar to what was recently observed in all-atom molecular dynamics simulations for classical models of water and also in experimental studies. Our results are explained in the framework of the two length scale potentials.

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.

Atomically detailed simulations of surface resistances to transport of CH4, CF4, and C2H6 through silicalite membranes

Abstract We have used atomically detailed methods to examine the surface resistances associated with single-component permeation of CH 4 , CF 4 , and C 2 H 6 through single crystal silicalite membranes. Dual control volume grand canonical molecular dynamics (DCV-GCMD) simulations can be used for this purpose, but only for extremely thin membranes and for relatively rapidly diffusing species. We use calculations of this type to introduce a more computationally efficient but approximate method for describing surface resistances, the local equilibrium flux method (LEFM). Using LEFM calculations, it is possible to accurately and rapidly predict surface resistances for large ranges of membrane operating conditions. Using this approach, we identify the crystal thicknesses beyond which surface resistances are negligible for single-component permeation of CH 4 , CF 4 , and C 2 H 6 through silicalite membranes as functions of membrane feed and permeate pressure.

Molecular Dynamics Simulations of Mass Transfer Resistance in Grain Boundaries of Twinned Zeolite Membranes

The net mass transfer resistance for gas molecules permeating through zeolite membranes includes contributions from intracrystalline diffusion and contributions from interfacial effects. These interfacial effects can arise either from gas-zeolite interfaces or from interfaces that exist within zeolite crystals due to grain boundaries. We present the first atomically detailed simulations that examine interfacial mass transfer resistance due to internal grain boundaries in zeolites that are relevant for membrane applications. Our calculations examine twinned silicalite crystals in crystallographic configurations that have been identified in previous experiments. We used the dual control volume grand canonical molecular dynamics method to simulate the permeance of CH(4) and CF(4) through thin twinned silicalite crystals. The magnitudes of the grain boundary resistances are quite substantial, at least for the thin crystals that are accessible in our simulations.

Non-equilibrium Molecular Dynamics Simulation on Pure Gas Permeability Through Carbon Membranes

The permeation of various pure gas (H 2, He, Ne, CH 4 and Ar) through carbon membranes is investigated using a dual control volume grand canonical molecular dynamics method. A two-dimensional slit pore is employed instead of the one-dimensional pore. Compared with the experiments, simulation results show that the improvement of pore model is very necessary. The effects of membrane thickness, pore width and temperature on gas permeance and ideal separation factor are also discussed. Results show that gas permeates through membrane according to Knudsen diffusion in large pore, while Knudsen diffusion is accompanied by molecular sieving in small pore. Moreover, methane is easily adsorbed on the membrane surface due to strong attractive interactions of membrane and shows higher permeance than that of Knudsen flow. In addition, it is noted that when membrane thickness is thin enough the permeance of gas does not decrease with the increase of membrane thickness due to the strong adsorption until membrane resistance becomes dominant.

Molecular dynamics simulation of gas permeation phenomena in a microporous silica membrane

In this study, the permeation phenomena of helium, nitrogen, and carbon dioxide gases are observed through dual control volume grand canonical molecular dynamics method, which is a combination of molecular dynamics simulation and grand canonical Monte Carlo method. Adsorption isotherm and angle distribution inside pores are analyzed to identify the permeation characteristics. Also, permeability and separation factor of pure gases and mixtures are investigated for the change of pressure, temperature, and composition. The predicted properties are compared with experimental data. The separation mechanisms of pure and mixture systems are identified through the analyses of simulation results.

Grand canonical Monte Carlo and non-equilibrium molecular dynamics simulation study on the selective adsorption and fluxes of oxygen/nitrogen gas mixtures through carbon membranes

The equilibrium selective adsorption and fluxes of oxygen/nitrogen binary gas mixtures through carbon membranes are investigated at 303 K, respectively, using a grand canonical Monte Carlo simulation and a dual control volume grand canonical molecular dynamics method. The carbon membrane pores are modeled as slit-like pores with a two-dimensional structure where carbon atoms are placed according to the structure of graphite layers. The effect of the membrane thickness, bulk pressure, and pore width on the equilibrium selective adsorption and dynamic separation factor is discussed. Meanwhile a new iteration approach to calculate the flux and dynamic separation factor of binary gas mixtures through membranes is proposed, by which we can simulate the permeation and fluxes of gases through the membranes in the presence of pressure gradient and consider the effect of pressure and composition of low-pressure side in the meantime. The simulated results show that bulk pressure and membrane thickness have no effect on the equilibrium selectivity, but they have a great effect on the fluxes and dynamic separation factors of gases. The pore width impacts the equilibrium selectivity and dynamic separation factors strongly, especially when the pore width is very small. Molecular sieving dominates the separation of oxygen/nitrogen in non-equilibrium simulations. But due to the comparable molecular size of oxygen and nitrogen, we have to modify the carbon membranes in order to improve dynamic separation of atmosphere.

Gas Permeation Through Zeolite Single Crystal Membranes

Diffusion of methane and argon mixtures through single crystal membranes is studied using the Dual-Control Volume-Grand Canonical Molecular Dynamics method. This study focuses on understanding the impact of crystal structure on surface resistance and membrane performance by comparing diffusion through silicalite, mordenite, AlPO4-5 and ZSM-12. Results showed that the contribution of surface resistance on membrane selectivity varies with the structure of the zeolite framework. Surface resistance is larger and longer range in silicalite, with an overall trend of silicalite > ZSM-12 > mordenite > AlPO4-5. This difference is attributed primarily to the smaller diameter of the silicalite pores, but the one-dimensional pore systems also seem to focus the translational momentum such that the surface resistance is smaller and shorter range.