Suitable pressures and temperatures for methane hydrate are found over
most of the seafloor but thermodynamic equilibrium imposes an additio
nal condition on the concentration of dissolved gas. We quantify the t
hermodynamic conditions for hydrate stability using a simulated anneal
ing algorithm to minimize the free energy of a mixture of methane gas
and seawater. The equilibrium state includes a description of the comp
osition of all stable phases as a function of pressure, temperature, a
nd salinity. When the hydrate phase is stable, we find that the equili
brium concentration of dissolved gas (solubility) decreases sharply wi
th temperature. The gas solubility is also lowered for typical values
of salinity in seawater. Since lower solubilities reduce the amount of
gas required to form hydrate, the presence of salts in seawater can a
ctually promote hydrate formation. Changes in salinity that accompany
hydrate formation add a thermodynamic degree of freedom, which permits
a three-phase zone to develop, where hydrate, seawater, and free gas
coexist over a range of temperatures at a constant pressure. We apply
our calculations to determine the location of stable phases in the sea
floor. The calculated profile of gas solubility permits hydrate to cry
stallize directly from dissolved gas in seawater. Diffusion of gas alo
ng the gradient in the equilibrium concentration implies a continual t
ransport of gas through the hydrate layer into the overlying ocean. In
order to maintain hydrate in the seafloor sediments, a persistant sou
rce of methane is required to overcome the losses due to diffusion. Ra
tes of hydrate growth and loss are estimated using simple models of ph
ysical conditions in marine sediments.