THEORETICAL JUSTIFICATION OF PHENOMENOLOGICAL LAW OF GAS FLOW RESISTANCE IN ROCK MASS
Rock mass saturated with gas can be assumed a thermodynamic system composed of elements which are ordered and connected by certain quantitative relations, and the set of the relations, that defines the connection between the elements of the system, governs the system structure. The experimental data prove that gas flow in porous media can be laminar, transient and turbulent; consequently, the equations of time–space distribution of pressure potential have different forms. Before a coal bed is exposed, the coal–gas system is in the steady-state nonequilibrium condition resistant relative to internal fluctuations. The system is closed as mass exchange with the ambient medium can be neglected, and only energy exchange takes place. The system structure is such that the amount and pressure of gas are dissimilar at different points of the coal bed, thus, the system is not in the condition of equilibrium. After exposure of the coal bed, the coal–gas system passes into a new steady-state nonequilibrium state which is characterized by an increase in the entropy and, as a consequence, is more unordered and stable. This article presents the generalized law of methane flow resistance in coal beds. This law is derived analytically and has a rigorous thermodynamic justification. Based on the principle of local equilibrium in systems, local equilibrium can be assumed in small macroscopic parts of a system; furthermore, it can be supposed that small areas of the system contain many particles, deviations from equilibrium are small, difference between the properties of the neighbor elements in the system is insignificant, and the processes in the system run slow. Small parts of the large coal–gas system exchange energy and particles. The phenomenological regularities of nonequilibrium thermodynamics allow deriving a generalized low of resistance for rock mass as the sum of gas flows governed by attenuation of gas flow, relaxation of gas pressure potential, gradients of pressure potentials and amount of adsorbed gas.
: Kachurin N. M., Ermakov A. Yu., Sencus Val. V.
Kachurin N.M., Doctor of Technical Sciences, Professor,
Head of Chair, Tula State University, 300012, Tula, Russia,
Ermakov A.Yu., Candidate of Technical Sciences, Manager of the Branch,
LLC «Sibniiugleobogaschenie», Prokopyevsk, Russia,
Sencus Val.V., Candidate of Technical Sciences, Head of Mining Department,
LLC «Proektgidrougol-H», Novokuznetsk, Russia.Key words
Theory, justification, phenomenological law, resistance, flow, gas, rock mass.References
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