(746i) Diffusion of Methane in SI Hydrates: A Kinetic Monte Carlo and Theoretical Study

Diffusion of Methane in sI Hydrates:
A Kinetic Monte Carlo and Theoretical Study

Lee-Shin Chu, David T. Wu† and Shiang-Tai Lin*

Department of Chemical Engineering,

National Taiwan University, Taipei, Taiwan

†Department of Chemical and Biological Engineering and
Department of Chemistry

Colorado School of Mines, Golden, CO, USA

R06524009@ntu.edu.tw, dwu@mines.edu, stlin@ntu.edu.tw

Abstract

Guest migration in clathrate hydrates is a
molecular-scale phenomenon. The transport of guest molecules in a hydrate
lattice is considered as a series of hopping events from an occupied cage to an
empty neighboring cage without significant lattice restructuring in the bulk.^1-3
Several studies have shown that the energy barrier for guest molecules hopping
through cages is remarkably reduced if a water vacancy exists in the water ring
at the interface shared by the donor and acceptor cages.^4-6 This
process is referred to as defect-driven diffusion. With evidence shown by
several simulation studies that the mobility of water vacancies in the hydrate
cages is much larger than that of the guest molecules^{4, 7}, it is
reasonable to assume that each hopping event of a guest molecule is driven by
the water vacancies in the hydrate lattice. In this work, kinetic Monte Carlo
(KMC) simulations of methane gas in sI hydrates were performed, with the
defect-driven hopping rate constants determined by Peters et al., based on
transition path sampling calculations [J. Am. Chem. Soc. 2008, 130 (51),
17342-17350.], as our input. The equilibrium occupancies, self and jump
(Maxwell-Stefan) diffusion coefficients and the thermodynamic correction
factors were estimated from our KMC simulations. In order to determine the
transport (Fick¡¦s) diffusion coefficient of methane gas in sI hydrates, an
analytical model is derived based on detailed balance and Maxwell-Stefan
diffusion theory, which relates the transport diffusion coefficients to the
known parameters, i.e., the hopping rate constants and the total occupancies
(occupied sites/available sites) of the hydrates. The analytical model agrees
well with the KMC simulation results. The estimated transport diffusion
coefficient at 273 K is 4.36*10^-14 m²/s, which is in good
agreement with the recent experimental measurements (4.00*10^-14 m²/s
at 275 K) by Salamatin et al.³

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