We have implemented a 2-dimensional numerical model for simulating gas hydrate and free gas accumulation in marine sediments. The starting equations are those of the conservation of the transport of momentum, energy, and mass, as well as those of the thermodynamics of methane hydrate stability and methane solubility in the pore-fluid. These constitutive equations are then integrated into a finite element in space, finite-difference in time scheme. We are then able to examine the formation and distribution of methane hydrate and free gas in a simple geologic framework, with respect to the geothermal heat flow, fluid flow, the methane in-situ production and basal flux. Three simulations are performed, leading to the build up of hydrate emplacements largely linear through time. Models act primarily as free gas accumulators and are relatively inefficient with respect to hydrate emplacements: 26–33% of formed methane are converted to hydrate. Seepage of methane across the sea-floor is negligible for fluid flow below 2. 10−11 kg/m2/s. At 5.625 10−11 kg/m2/s however, 9.7% of the formed methane seeps out of the model. Moreover, along strike variation arising in the 2-dimensional model are outlined. In the absence of focused flow, the thermodynamics of hydrate accumulation are primarily one-dimensional. However, changes in free methane compressibility (density) and methane solubility (the intrinsic dissolved methane flux) subtlety impact on the formation of a free gas zone and the distribution of the hydrate emplacements in our 2-dimensional simulations.