  A two-phase two-component model is formulated for the advective-diffusive
transport of methane in liquid phase through sediment with the accompanying
formation and dissolution of methane hydrate. This free-boundary problem has a
unique generalized solution in $L^1$; the proof combines analysis of the
stationary semilinear elliptic Dirichlet problem with the nonlinear semigroup
theory in Banach space for an m-accretive multi-valued operator. Additional
estimates of maximum principle type are obtained, and these permit appropriate
maximal extensions of the phase-change relations. An example with pure
advection indicates the limitations of these estimates and of the model
developed here. We also consider and analyze the coupled pressure equation that
determines the advective flux in the transport model.
