On a problem of nonvariant equilibrium of phase ice-hydrate transformation

The work presents a thermodynamically equilibrium filtration model for the gas-hydrate phase-equilibrium (nonvariant) and hydrate-thaw zones with two components (Н2О, gas), taking into account the ice-water phase transition. The Н2О components (liquid water and ice) and the gas outside the hydrate form a water-ice and gas mixture in a porous medium. The study of hydrates in the permafrost zone is of great practical importance for understanding the processes associated with climate change. To implement the model proposed in the work, the method of splitting by physical processes is applied; the system is transformed to a block form with the separation of the dissipative and hyperbolic parts. The developed mathematical model is common for the entire area of the process and makes it possible to study gas-hydrate and water-ice phase transitions due to the use of the original enthalpy form of the piezoconductivity equation. The change in the enthalpy value in the internal process of the phase transformation of the water-ice mixture makes it possible to model the internal evolution of phase transitions, in particular, the volume fractions of the water-ice structure. For this model, its discretization has been performed. Discrete algorithms are integrally consistent, which allows maintaining the exact balance of mass components (Н$_2$О, gas) and the total internal energy of the entire system at the difference level. Program implementation has been developed, with the help of which a series of calculations has been carried out. Calculations have shown that in the water-ice zone, over time, a phase ice-hydrate transformation occurs with the melting of ice, which is energetically compensated by the formation of hydrate.