Path Sampling Calculation of Methane Diffusivity in Natural Gas Hydrates from a Water-Vacancy Assisted Mechanism

Abstract

Increased interest in natural gas hydrate formation and decomposition, coupled with experimental difficulties in diffusion measurements, makes estimating transport properties in hydrates an important technological challenge. This research uses an equilibrium path sampling method for free energy calculations [Radhakrishnan, R.; Schlick, T. J. Chem. Phys. 2004, 121, 2436] with reactive flux and kinetic Monte Carlo simulations to estimate the methane diffusivity within a structure I gas hydrate crystal. The calculations support a water-vacancy assisted diffusion mechanism where methane hops from an occupied "donor" cage to an adjacent "acceptor" cage. For pathways between cages that are separated by five-membered water rings, the free energy landscape has a high barrier with a shallow well at the top. For pathways between cages that are separated by six-membered water rings, the free energy calculations show a lower barrier with no stable intermediate. Reactive flux simulations confirm that many reactive trajectories become trapped in the shallow intermediate at the top of the barrier leading to a small transmission coefficient for these paths. Stable intermediate configurations are identified as doubly occupied off-pathway cages and methane occupying the position of a water vacancy. Rate constants are computed and used to simulate self-diffusion with a kinetic Monte Carlo algorithm. Self-diffusion rates were much slower than the Einstein estimate because of lattice connectivity and methane's preference for large cages over small cages. Specifically, the fastest pathways for methane hopping are arranged in parallel (nonintersecting) channels, so methane must hop via a slow pathway to escape the channel. From a computational perspective, this paper demonstrates that equilibrium path sampling can compute free energies for a broader class of coordinates than umbrella sampling with molecular dynamics. From a technological perspective, this paper provides one estimate for an important transport property that has been difficult to measure. In a hydrate I crystal at 250 K with nearly all cages occupied by methane, we estimate D approximately 7 x 10(-15) X m(2)/s where X is the fraction of unoccupied cages.

Inter-cage dynamics in structure I, II, and H fluoromethane hydrates as studied by NMR and molecular dynamics simulations

“…42 The CH 3 F · · · HOH binding energy was determined to be similar to water dimer and the F · · · H distance is 1.9926 Å which is consistent with hydrogen bonding. Special host-guest interactions 43 (i.e., halogen bonding 17 as, for example, in the hydrates of dihalogens), 44 may contribute to this hydrogen bonding so that the combination of TBME and CH 3 F also may give rise to fast dynamics of the water lattice. Recent calculations of CH 4 diffusivity in a hydrate lattice 44 have introduced water vacancies in the hydrate lattice in order to get reasonable rates of transport.…”

Transport into Nanosheets: Diffusion Equations Put to Test

“…Despite this problem, we find that it is sufficient to start the RF simulations from the surface barrier ("O" in Figure S9) and stop a given shoot if the molecule has reached either the center plane of the outermost cage (z = 2.95 nm) or if it has left the simulation box at the left hand-side end at z = 6.34 nm. Evidence comes from probability distributions that track the temporal evolution of the entire swarm of RF trajectories, 41,42 as displayed in Figure S10. Only a very small fraction of the swarm aims for the surface adsorption site, which is again marked with an "X" (blue).…”

On the Effects of the External Surface on the Equilibrium Transport in Zeolite Crystals

“…H is the Heaviside function (H(x) ) 1 for x g 0 and H(x) ) 0 otherwise). Starting configurations for the RFCFs were generated using an MD-based approach (BOLAS 35 and EPS 36 ). Otherwise, the procedure for the RFCF simulations is the same as in ref 4.…”