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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. [ABSTRACT FROM AUTHOR]

The Peng-Robinson equation of state (PR-EOS) (Robinson and Peng 1978) with capillary effect has been used extensively to describe the phase behavior of hydrocarbons under nanoconfinement in shale reservoirs. In nanopores, surface adsorption may be significant, and molecular distribution is heterogeneous. Although the PR-EOS cannot consider these effects, statistical thermodynamic approaches such as density-functional theory (DFT) can explicitly consider the intermolecular and fluid/surface interactions. In this work, we compare the phase behavior of pure hydrocarbons and mixtures in nanopores from the PR-EOS with capillary effect and engineering DFT. We apply the Young-Laplace (YL) equation, assuming zero contact angle to calculate the capillary pressure in the PR-EOS with capillary effect. On the other hand, we extend the PR-EOS to inhomogeneous conditions with weighted-density approximation (WDA) in engineering DFT. For pure components, both approaches predict that the dewpoint temperature increases in hydrocarbon-wet nanopores. Although engineering DFT predicts that the confined dewpoint temperature approaches bulk saturation point when pore size approaches 30 nm, the saturation point obtained from the PR-EOS with capillary effect approaches bulk only when the pore size is as large as 1000 nm. With engineering DFT, the critical points in nanopores deviate from those in bulk, but no change is observed from the PR-EOS with capillary-effect model. The difference on the dewpoint temperature between the PR-EOS with capillary effect and engineering DFT decreases as the system pressure approaches the critical pressure. At low-pressure conditions, the PR-EOS with capillary-effect model becomes unreliable. For binary mixtures, both approaches predict that the lower dewpoint decreases and the upper dewpoint increases. More interestingly, phase transition can still occur when the system temperature is higher than the bulk cricondentherm point. Engineering DFT predicts that the confined lower dewpoint approaches bulk when pore size approaches 20 nm, whereas the dewpoint obtained from the PR-EOS with capillary effect approaches bulk only when the pore size is as large as 100 nm. This work illustrates that assuming homogeneous distributions in nanopores may not be appropriate to predict the phase behavior of hydrocarbons under nanoconfinement. [ABSTRACT FROM AUTHOR]

The article looks at the study related to use of density functional theory for finding phase behavior and adsorption of pure substances and mixtures and characterization in nanopore structures. It mentions use of engineering density functional theory (DFT) combined with the Peng-Robinson equation of state (EOS) to investigate the adsorption and phase behavior of pure substances and mixtures in nanopores.

Porous carbons of high surface area are promising as cost-effective electrode materials for supercapacitors. Although great attention has been given to the anomalous increase of the capacitance as the pore size approaches the ionic dimensions, there remains a lack of full comprehension of the size dependence of the capacitance in nanopores. Here we predict from a classical density functional theory that the capacitance of an ionic-liquid electrolyte inside a nanopore oscillates with a decaying envelope as the pore size increases. The oscillatory behavior can be attributed to the interference of the overlapping electric double layers (EDLs); namely, the maxima in capacitance appear when superposition of the two EDLs is most constructive. The theoretical prediction agrees well with the experiment when the pore size is less than twice the ionic diameter. Confirmation of the entire oscillatory spectrum invites future experiments with a precise control of the pore size from micro- to mesoscales. [ABSTRACT FROM AUTHOR]

Entropic force has been a focus of many recent theoretical studies because of its fundamental importance in solution thermodynamics and its close relevance to a broad range of practical applications. Whereas previous investigations are mostly concerned with the potential energy as a one-dimensional function of the separation, here we propose a hybrid method for studying multidimensional systems by combining Monte Carlo simulation for the microscopic configurations of the solvent and the density functional theory for the free energy. We demonstrate that the hybrid method predicts the potential of mean force between a test particle and various concave objects in a hard-sphere solvent in excellent agreement with the results from alternative but more expensive computational methods. In particular, the hybrid method captures the entropic force between asymmetric particles and its dependence on the particle size and shape that underlies the “lock and key” interactions. Because the same molecular model is used for the theory and simulation, we expect that the hybrid method provides a new avenue to efficient computation of entropic forces in complex molecular systems. [ABSTRACT FROM AUTHOR]