On the Thermodynamic Stability of Clathrate Hydrates VI: Complete Phase Diagram.

We develop a method to evaluate the thermodynamic stability of clathrate hydrates relative to host water and/or guest species. This enables to investigate complete phase behaviors of clathrate hydrates in the whole space of the thermodynamic variables, not only temperature and pressure but also composition, with only the intermolecular interactions as input parameters. A complete phase diagram of clathrate hydrate is settled with this method, specifically the region enclosed by the hydrate/water and hydrate/guest phase boundaries where a clathrate hydrate is the only stable phase. The method is applied to methane clathrate hydrate, which results in an excellent agreement in dissociation pressure with the experimental observations. It is found that the hydrate/water phase boundary is significantly affected by the phase transition of water from ice to liquid. This transition limits the stable area of the clathrate hydrate terminated at the dissociation temperature, which otherwise exhibits unphysical divergence. It is essential to choose a pressure as an independent variable so as to calculate the accurate phase equilibria in composition space. The present method establishes a pressure-temperature-composition relation for a single stable phase of clathrate hydrate as well as recovering its temperature dependence of the dissociation pressure.