Abstract:
In this work, the method of splitting by physical processes is consistently applied to the
problems of underground hydromechanics related to gas hydrates and taking into account
the presence of ice and the ice-water phase transition, as well as the presence of salt and
gas dissolved in water. The systems are reduced to a block form, with the separation of
the dissipative and hyperbolic parts. It is shown by the method of characteristics that the
usual approximation of the upstream coefficients must be modified here. Using the Gibbs
phase rule, the choice of governing variables in flow zones that differ from each other in
the number of phases and components is made. A general mathematical model has been
constructed for the entire process flow area, which takes into account the dynamic appearance and disappearance of such zones as a result of filtration and phase transitions.
Based on the developed discrete algorithms, the problem of the interaction of a vertical
fault and a horizontal reservoir containing a gas hydrate with a dynamic transition of the
hydrate-equilibrium and thawed zones is numerically studied.
Keywords:mathematical modeling, gas hydrates, multicomponent filtration, permafrost.