Gas hydrates are ice-like crystalline solids composed of a hydrogen bonded water lattice entrapping low-molecular weighted gas molecules commonly of methane. These form under conditions of relative high pressure and low temperature, when the gas concentration exceeds those which can be held in solution, both in marine and on-land permafrost sediments. Simulating the mechanisms leading to natural gas hydrate emplacement in geological environments requires the modeling of the temperature, the pressure, the chemical reactions, and the convective/diffusive flow of the reactive species. In this study, we take into account the distribution of dissolved methane, methane gas, methane hydrate, and seawater, while ice and water vapor are neglected. The starting equations are those of the conservation of the transport of momentum (Darcy’s law), energy (heat balance of the passive sediments and active reactive species), and mass. These constitutive equations are then integrated into a 2-dimentional finite element in space, finite-difference in time scheme. In this study, we are able to examine the formation and distribution of methane hydrate and free gas in a simple geologic framework, with respect to geothermal gradient, dewatering and fluid flow, the methane in-situ production and basal flux. The temperature and pressure fields are mildly affected by the hydrate emplacement. The most critical parameter in the model appears to be the methane (L+G) and hydrate (L+G+H) solubility: the decrease in methane solubility beneath the base of the hydrate stability zone (BHSZ) critically impacts on the presence of free gas at the base of the BHSZ (thus the presence of a BSR), while the sharp decrease of hydrate solubility above the BHSZ up to the sea bottom critically impact on the amount of methane available for hydrate emplacement and methane seep into the water column.