Analysis of change in the number of gas molecules in an elementary volume of rock mass shows that as a consequence of collision of gas molecules and rocks and owing to sorption–desorption reactions between them, the phase-space distributions of molecules of free and adsorbed gas are statistically interrelated, and, for this reason, in conformity with the principle of local equilibrium for an arbitrary point in rock mass, the deviation of the distribution function of free gas molecules from the Maxwell distribution will be insignificant. At the same time, due to desorption, the second group will drag in molecules which fall beyond the first group at a given time. The analytical equation is obtained to describe gas transfer in coal beds and enclosing rocks at the molecular scale in pursuance and entailment of the fundamental provision of the theory of kinetic equations. The equations of gas flow in a porous gas-adsorbing medium disregard dispersion of macroscopic fields of true density of free gas and fluctuation due to the irregularity of the transfer velocity field, while the kinetic equation of distribution function of free gas molecules in phase space takes this specificity into account. Going from the distribution function to the first order moment allows localization of the equation and mathematical model of gas flow process with the unknown quantities represented by macroscopic characteristics of density or pressure of free gas. The mathematical model of gas transfer in a gas-adsorbing porous medium, to be suitable for the scientific substantiation of applied problems, should contain generally accepted macroscopic characteristics of thermodynamic state of gas. Thus, it is required to find connections between the effective characteristics of seepage transfer and density field of free gas.

**Keywords**

Model, physical, mathematical, methane transfer, rock mass, gas-adsorbing rocks.

**Issue number**: 5 **Year**: 2018 **ISBN**: **UDK**: 622.831 **DOI**: 10.25018/0236-1493-2018-5-0-81-88 **Authors**: Ermakov A. Yu., Kachurin N. M., Sencus Val. V.

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