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We determine thermodynamic stability conditions in terms of Helmholtz andGibbs energies for sI clathrate hydrates with CH$_4$ and CO$_2$ at 278 K.Helmholtz energies are relevant for processing from porous rocks (constantvolume), while Gibbs energies are relevant for processing from layers on theocean floor (constant pressure). We define three steps leading to hydrateformation, and find Helmholtz energy differences from molecular simulations fortwo of them using grand-canonical Monte Carlo simulations at constanttemperature and volume; while the third step was calculated from literaturedata. The Gibbs energy change for the same steps are also determined. From thevariations in the total Helmholtz and Gibbs energies we suggest thermodynamicpaths for exchange of CH$_4$ by CO$_2$ in the isothermal hydrate, for constantvolume or pressure, respectively. We show how these paths for the mixed hydratecan be understood from single-component occupancy isotherms, where CO$_2$, butnot CH$_4$, can distinguish between large and small cages. The strongpreference for CH$_4$ for a range of compositions can be explained by these.

Gibbs and Helmholtz energies of formation of sI clathrate hydrates from CO$_2$, CH$_4$ and water