Methodology for Calculating the Parameters of Non-isothermal Filtration Considering the CO\({}_{\mathbf{2}}\)–CH\({}_{\mathbf{4}}\) Replacement in Methane Hydrate

A mathematical model of non-isothermal filtration of methane, carbon dioxide and water is constructed based on the methods and equations of multiphase media mechanics considering the replacement of methane in the gas hydrate with carbon dioxide. The equations of the mathematical model and the methodology for their numerical solution are presented. The numerical solutions for one-dimensional plane-parallel approximation are constructed for the problem of injecting carbon dioxide into a reservoir initially saturated with methane and its hydrate. Those solutions describe the distributions in the reservoir of pressure, temperature, mass concentrations of gas phase components and saturations of methane and carbon dioxide hydrates.