Warming, degradation of ice cover, and an increased abundance of thermogenic gas hydrates in rapidly warming regions of polar shelves may contribute to modifications of the carbon cycle in bottom sediments and the water column through the vertical migration of deep hydrocarbons into near-bottom horizons. In this study, numerical modeling of free methane migration through a sediment column characterized by gas hydrate stability zone conditions is performed to assess the potential input of additional carbon into bottom sediment structures and the water column. To analyze these processes, a mathematical filtration model describing fluid behavior in a porous medium is developed, with a mathematical framework based on a system of partial differential equations accounting for coupled gas–liquid flow, the presence of a gas hydrate phase, and phase transitions. The modeling, carried out using the laws of mass and energy conservation in combination with Darcy’s law, made it possible to trace changes in the configuration of the gas hydrate stability zone during the vertical migration of methane from deep horizons toward the seafloor. A quantitative assessment of the potential input of deep carbon has been performed for the shelf area of the Ross Sea (Antarctica) using a numerical approach under the assumption of local thermodynamic equilibrium. It is shown that an ascending flux of free gas can traverse the gas hydrate stability zone while undergoing only partial conversion into the hydrate phase, followed by further migration into the water column; as a result, a three-phase equilibrium zone (gas–hydrate–water) is formed, which gradually replaces the initial two-phase system (hydrate–water). The modeling-based results help explain the discrepancies between radiocarbon dating of sediment cores and ice-sheet history reconstructions in the studied region.

mathematical modeling, gas hydrate stability zone, methane vertical filtration, phase transitions in porous media, multicomponent fluid dynamics

Mathematical modelling in actual problems of science and technics