On a Problem of Invariant Equilibrium of a Phase Ice-Hydrate Transformation

This study presents a thermodynamically equilibrium filtration model for the gas-hydrate phase-equilibrium (invariant) 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 significant practical importance for understanding the processes related to climate change. To implement the model proposed in this study, the method of splitting by physical processes is applied; and 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. This model is discretized. Discrete algorithms are integrally consistent, which allows maintaining the exact balance of the mass components (Н₂О, gas) and the total internal energy of the entire system at the difference level. A software implementation is developed, with the help of which a series of calculations are carried out. The calculations show 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 a hydrate.