Mathematical Model of Injection of Carbon Dioxide into a Gas-Hydrate-Bearing Formation

A mathematical model was presented to describe the injection of "warm" carbon dioxide into a porous geological formation that is initially saturated with methane and its hydrate with a negative (below the melting point of ice) temperature. A scheme in which three regions emerge in the formation was considered: a near region, which contains carbon dioxide and its gas hydrate; an intermediate region, which contains methane and ice; and a far region, which is saturated with methane and its hydrate. A system of equations was proposed, which included a continuity equation, a heat input equation, and Darcy's law. Using this system, the effect of the initial pressure in the formation and its permeability on the mechanisms of generation of carbon dioxide hydrate was studied. Based on the obtained self-similar solutions, it was determined that the generation of CO2 hydrate may occur by qualitatively different mechanisms, depending on the initial pressure in the system or the permeability of the formation. At low initial pressures, CH4 hydrate decomposes into ice and methane, and CO2 hydrate forms from ice and carbon dioxide. At low formation permeabilities, the generation of from water and carbon dioxide is accompanied by the emergence of an additional (fourth) region saturated with methane and water. Moreover, there may be a mechanism by which methane hydrate decomposes into water and gas, carbon dioxide hydrate forms from CO2 and water, and three regions emerge. At high formation permeabilities and high initial pressures, carbon dioxide hydrate forms by a substitution mechanism, i.e., a direct transition of methane hydrate to carbon dioxide hydrate.