We describe a method for calculating free energies and chemical potentials for molecular models of gas hydrate systems using Monte Carlo simulations. The method has two components: (i) thermodynamic integration to obtain the water and guest molecule chemical potentials as functions of the hydrate occupancy; (ii) calculation of the free energy of the zero-occupancy hydrate system using thermodynamic integration from an Einstein crystal reference state. The approach is applicable to any classical molecular model of a hydrate. We illustrate the methodology with an application to the structure-I methane hydrate using two molecular models. Results from the method are also used to assess approximations in the van der WaalsPlatteeuw theory and some of its extensions. It is shown that the success of the van der Waals-Platteeuw theory is in part due to a cancellation of the error arising from the assumption of a fixed configuration of water molecules in the hydrate framework with that arising from the neglect of methane-methane interactions.

We describe a calculation of the phase behavior of the methane-water system, including the structure-I hydrate phase, starting from a model of the intermolecular forces in the system and using Monte Carlo simulations and theory. The approach we use differs from previous calculations of methane hydrate phase behavior in that it does not treat the water molecules in the hydrate as a static or harmonic lattice, i.e., thermal fluctuations are fully incorporated. Our approach is quite general, but we illustrate it here for perhaps the simplest model capable of forming stable hydrate-like structures. This is a mixture of network-forming associating hard spheres and nonassociating hard spheres. With this model as a reference system, we add dispersion forces and dipole-dipole interactions as perturbations. Monte Carlo simulations were used to determine the solid-phase properties of this model, and the fluid phases were treated using an accurate thermodynamic perturbation theory. Our results show that this simple molecular model is able to describe the phase diagram in qualitative agreement with the experiment. In particular, it correctly describes the region of stability of a single-phase methane structure-I hydrate and its dependence on temperature, pressure, and composition.

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