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

Starting from the orthogonal dynamics of any given set of variables with respect to the projection variable used to derive the Mori–Zwanzig equation, a set of coupled Volterra equations is obtained that relate the projected time correlation functions between all the variables of interest. This set of equations can be solved using standard numerical inversion methods for Volterra equations, leading to a very convenient yet efficient strategy to obtain any projected time correlation function or contribution to the memory kernel entering a generalized Langevin equation. Using this strategy, the memory kernel related to the diffusion of tagged particles in a bulk Lennard–Jones fluid is investigated up to the long-term regime to show that the repulsive–attractive cross-contribution to memory effects represents a small but non-zero contribution to the self-diffusion coefficient. [ABSTRACT FROM AUTHOR]

Understanding drying processes in nanoporous media is of great importance in many technological and industrial situations. To better understand how gas moves through clayey rocks, of interest for underground disposal of radioactive wastes, we propose using pore-scale direct numerical simulations. In this study, we use the Smoothed Particle Hydrodynamics method, which has proved to be an effective approach for simulating complex fluid dynamics within porous media at the nanoscale. Our simulations consider capillary-dominated two-phase flow with evaporation and condensation at liquid–gas interfaces, coupled to the diffusion of water vapor in the gas phase, as well as the Kelvin effect, which is a specific feature of nanopores. Our evaporation-condensation model is validated against analytical solutions. The size of the compact support of kernel function and the particle density required to obtain accurate and stable results of capillary pressure are investigated. Drying regimes, capillary-driven and evaporated-driven, are explored. A specific effort is made to highlight the influence of the Kelvin effect on desaturation and the creation of preferential paths for gas flow as well as its impact on drying rate. The role of condensation due to local vapor concentration conditions is also emphasized. [ABSTRACT FROM AUTHOR]