Mathematical model and algorithm for solving the problem of non-isothermal gas filtration in reservoir in case of hydrate decomposition

The paper formulates a problem of injection into porous bed, filled up in the initial condition with hydrate and gas, warm (with the temperature higher than the initial temperature of the bed) gas. A mathematical model of non-isothermal gas filtration in case of gas hydrate dissociation is developed to solve this problem. The article presents a solution algorithm, where an implicit difference scheme, a sweep method and a method of simple integration are applied. The method for calculating hydrate saturation from several limiting conditions is suggested. It can be used for solution of other phase-change problems, also for multidimensional Stefan problems, as well as problems with an extended phase transition zone. After that the problem is considered in one-dimensional plane-parallel formulation with regard to required initial and boundary conditions for finding a computational solution of a set of equations describing this model. At the end, the paper presents the problem calculation results using the suggested method, on the basis of which the distribution of parameter values for some time intervals are shown. In the performed calculations the reservoir in the initial condition is filled up with methane and its hydrate.