The theoretical model is considered in the one-dimensional approximations and numerical solutions are obtained for the process of replacing methane with carbon dioxide from a hydrate in a formation saturated with methane and its hydrate when carbon dioxide is injected into the formation. The process is considered under thermobaric conditions corresponding to the stability region of methane gas and carbon dioxide and the region of existence of CO2 in the form of a gaseous phase. The case is considered when the rate of carbon dioxide hydrate formation is limited by diffusion of carbon dioxide through the formed hydrate layer between the gas mixture stream and methane hydrate. It is accepted that the hydration substitution process occurs without the release of water from the hydrate. To describe the mathematical model, the main equations are the mass conservation equations for methane, carbon dioxide and their hydrates, Darcy’s law for filtration, Fick’s law for diffusive mixing of the gas mixture, state equations for the gas phase, Dalton’s law, energy equation, diffusion equation for transport CO2 through the hydration layer at the pore microchannel scale. The dynamics of the mass flow rates of the outgoing carbon dioxide and methane recovered has been investigated. The influence of the diffusion coefficient, the absolute permeability and the length of the formation on the intensity of the methane produced as a result of the gas substitution process is analyzed. Three main stages of the process were identified: displacement of free methane from the reservoir; extraction of free methane obtained as a result of the beginning of hydrate substitution in the formation; complete conversion of methane hydrate to carbon dioxide hydrate and complete extraction of methane from the formation. It is determined how the two main factors relate to each other in terms of the degree of influence on the replacement rate: heat and mass transfer in the reservoir and the kinetics of the replacement process.
Gas Hydrate Formation Process for Capture of Carbon Dioxide from Fuel Gas Mixture