  We study the transport of methane in the external water envelopes surrounding
water-rich super-Earths and estimate its outgassing into the atmosphere. We
investigate the influence of methane on the thermodynamics and mechanics of the
water mantle. We find that including methane in the water matrix introduces a
new phase (filled ice) resulting in hotter planetary interiors. This effect
renders the super-ionic and reticulating phases accessible to relatively low
mass planets lacking a H/He atmosphere. We model the thermal and structural
profile of the planetary crust and discuss five possible crustal regimes. The
formation of methane clathrate in the subsurface is shown to inhibit the
formation of a subterranean ocean. This effect results in increased stresses on
the lithosphere making modes of ice plate tectonics possible. The dynamics of
the tectonic plates are analysed. We derive overturn and resurfacing time
scales as well as the melt fraction underneath spreading centers. Ice mantle
dynamics is found to be important for assessing the composition of the
atmosphere. We formulate the relation between the outgassing flux of methane
and the tectonic mode dynamics. We give numerical estimates for the global
outgassing rate of methane into the atmosphere.
