Mathematical Model of Decomposition of Methane Hydrate during the Injection of Liquid Carbon Dioxide into a Reservoir Saturated with Methane and Its Hydrate

• Main Authors: Marat K. Khasanov, Nail G. Musakaev, Maxim V. Stolpovsky, Svetlana R. Kildibaeva
• Format: Article
• Language: English
• Published: MDPI AG 2020-09-01
• Series: Mathematics
• Subjects: mathematical model; multiphase flows; flow in porous media; gas hydrate; filtration
• Online Access: https://www.mdpi.com/2227-7390/8/9/1482

The article describes a mathematical model of pumping of heated liquid carbon dioxide into a reservoir of finite extent, the pores of which in the initial state contain methane and methane gas hydrate. This model takes into account the existence in the reservoir of three characteristic regions. We call the first region “near”, the second “intermediate”, and the third “far”. According to the problem statement, the first region contains liquid CO₂ and hydrate, the second region is saturated with methane and water, the third contains methane and hydrate. The main features of mathematical models that provide a consistent description of the considered processes are investigated. It was found that at sufficiently high injection pressures and low pressures at the right reservoir boundary, the boundary of carbon dioxide hydrate formation can come up with the boundary of methane gas hydrate decomposition. It is also shown that at sufficiently low values of pressure of injection of carbon dioxide and pressure at the right boundary of the reservoir, the pressure at the boundary of hydrate formation of carbon dioxide drops below the boiling pressure of carbon dioxide. In this case, for a consistent description of the considered processes, it is necessary to correct the mathematical model in order to take into account the boiling of carbon dioxide. Maps of possible solutions have been built, which show in what ranges of parameters one or another mathematical model is consistent.