Mathematical Model and Method for Solving the Problem of Non-Isothermal Gas and Liquid Filtration Flow During Dissociation of Gas Hydrates

The development of a mathematical model of the filtration flow during dissociation of gas hydrates for the two-dimensional case is researched considering the motion of both components of the gas hydrate (water and gas). Non-isothermal effects and the gas being not ideal while filtering liquid and gas are considered; the hydrate dissociation process is assumed to be in equilibrium. A method is developed for solving the system of equations of the mathematical model using an implicit difference scheme, tridiagonal matrix algorithm and simple iterations, as well as a developed method for calculating hydrate saturation. This method allows to find the spatial distributions of the main parameters of the gas-liquid filtration flow (temperature, pressure and phases saturations) for each moment in time, as well as position of the boundary of phase transitions.