Mathematical modeling of gas hydrate dissociation in porous medium taking into account ice and salinity

This work is devoted to the mathematical modeling of the dissociation of gas hydrates in a porous medium. Numerical methods are developed for solving problems of underground hydromechanics associated with gas hydrates in the permafrost zone of northern regions and on the shelf of the Arctic seas. The considered system of equations takes into account the presence of ice and ice–water phase transitions, as well as the presence of salt. Using the method of splitting by physical processes, the system is transformed into a block form, in which the dissipative and hyperbolic parts are separated. As a result, its own numerical approach can be effectively applied to each block. In the final algorithm, zones characterized by a different set of equations and independent variables are identified. A thermodynamic analysis of the physical processes and mathematical coordination of the problems in the zones are carried out to enhance the stability of the method. As a result, a unified computational scheme is built and test calculations are carried out. An analysis of the results confirms the effectiveness of the developed numerical approach.