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PHYSICAL MODEL AND MATHEMATICAL DESCRIPTION OF METHANE MOTION IN MINING MASSIF TAKING INTO ACCOUNT FINAL PRESSURE SPEED

The physical model and the mathematical description of the methane movement in the rock massif are substantiated, taking into account the final pressure propagation velocity. It is proved that the mathematical model of gas filtration in coal seams and host rocks is based on an equation of hyperbolic type and it is shown that the use of parabolic type equations is physically justifiedfor long periods of time. It is proposed to use the law of resistance, which is a functional relationship between the gas flow and the gas pressure gradient and the local rate of change of the gas flow for an arbitrarily selected point in the considered region of the rock mass. The derivation of non-linear equations of the hyperbolic type for modeling methane filtration in coal seams and host rocks is presented. Variants of linearized equations of hyperbolic type for modeling methane filtration are presented and their use as approximate mathematical models is recommended.