Nonequilibrium Thermodynamics of Hydrate Growth on a Gas-Liquid Interface

We develop a continuum-scale phase-field model to study gas-liquid-hydrate systems far from thermodynamic equilibrium. We design a Gibbs free energy functional for methane-water mixtures that recovers the isobaric temperature-composition phase diagram under thermodynamic equilibrium conditions. The proposed free energy is incorporated into a phase-field model to study the dynamics of hydrate formation on a gas-liquid interface. We elucidate the role of initial aqueous concentration in determining the direction of hydrate growth at the interface, in agreement with experimental observations. Our model also reveals two stages of hydrate growth at an interface—controlled by a crossover in how methane is supplied from the gas and liquid phases—which could explain the persistence of gas conduits in hydrate-bearing sediments and other nonequilibrium phenomena commonly observed in natural methane hydrate systems.

Figure 1

(a) Burning of solid (white) methane hydrate (source: USGS). (b) Isobaric methane-water $T–\chi$ phase diagram adapted from [5, 6].

Figure 2

(a) Gibbs free energy of all phases at various temperatures: green and red dots, equilibrium compositions; dashed grey lines, common tangents. At 5 MPa, (b) analytically calculated $T–\chi$ phase diagram; (c) enlarged version of the shaded grey area in (b); at 30 MPa, focusing on the hydrate-forming region, (d) analytically calculated $T–\chi$ phase diagram; (e) $T–\chi$ phase diagram from experiments adapted from [5]. The dashed line marks $T^T$ in all figures. (f) The division of the $\chi$ axis into five phase regions by four equilibrium points (orange), not drawn to scale. The grey points correspond to gas-liquid equilibrium, which is not feasible under hydrate-forming scenarios.

Figure 3

(a) Schematic illustrating hydrate growth on a liquid-gas interface. Simulated profiles of ${\varphi }_s$ at different times (grey scale) and initial profile of $\chi$ (red) for (b) initially supersaturated liquid and (c) initially undersaturated liquid. The black arrow points to growth direction and the black dot marks the position of initial gas-liquid interface. (d) Domain-integrated ${\varphi }_s$ over time. [(e) and (f)] Domain-integrated hydrate growth rate (black) and gas consumption rate (blue) as a function of time, with gas-sustained (purple) and liquid-sustained (green) stages of hydrate growth.

Figure 4

Simulations illustrating hydrate-encased gas conduits forming in initially undersaturated liquid (${\chi }_l^0=0.005<{\chi }_l^{gl}$). Simulation (a) corresponds to a pressure difference driving the flow that is twice that of simulation (b).