Vast quantities of clathrate hydrate are found in the Arctic and in ma
rine sediments along continental margins. The clathrate structure trap
s enormous volumes of methane gas, which is both a possible source of
global climate change and a potential energy resource. The growth rate
and spatial distribution of gas hydrate in the shallow sediments are
influenced by a variety of interacting physical processes. In order to
quantify these processes, we develop mathematical models for hydrate
formation in porous media. An analytical model is derived for the idea
lized problem of hydrate growth in a porous half-space which is cooled
on its boundary. Our calculations predict the growth rate of a hydrat
e layer for a given rate of cooling and show that the volume of hydrat
e is strongly dependent on the two-phase equilibrium between hydrate a
nd seawater. For a representative phase diagram we find that the volum
e of hydrate in the layer is less than 1% of the pore volume. Larger v
olumes of hydrate observed in some locations demand a sustained supply
of gas and a long accumulation time. Numerical calculations are used
to investigate situations that are more representative of conditions i
n marine sediments. A simple theoretical expression is derived for the
rate of hydrate accumulation due to advection of methane gas from dep
th. Using typical estimates of fluid velocities in accretionary enviro
nments, we obtain an accumulation rate of 1% of the pore volume in 10(
5) years. The predicted vertical distribution of hydrate is consistent
with geophysical inferences from observed hydrate occurrences along t
he Cascadia margin. Similar distributions can arise from the combined
effects of in situ methane production and warming due to ongoing sedim
entation. Predicted differences between these two formation models may
be detectable in geophysical and geochemical measurements.