Rarefaction shock waves in porous media that accumulate CO2, CH4, N2

In this paper, a porous medium whose core is built from a solid substance is considered. Such a medium can accumulate liquid and gaseous substances absorbing on the surface of the solid body and diffusing within its molecular lattice. The medium forms a so-called solid solution. A change in the values of the thermodynamic parameters of this medium leads to phase transitions in these substances. Besides, some other associated phenomena may occur. There are given the results of laboratory analyses concerning the relation between the specific volumeV of the solid solution formed by the coal with CO₂, CH₄, N₂ dissolved in it and its confining pressurep. This relation indicates the possibility of the propagation of a rarefaction shock waves in such a medium.A mathematical model of the generation of such waves and its specific applications to describe the initial boundary conditions affected during the experiments presented. The results of these experiments have confirmed the adopted model, particularly those aspects that are concerned with the specific sliced structures of the coal medium with the accumulated CO₂ and N₂, through which a rarefaction shock wave has passed (Figs. 10a, 10b, 11a, and 11b). The presented model explains the phenomena of sudden massive rock-and-gas outbursts, occurring in nature, e.g. as a result of disturbing the primary equilibrium of the rocks in the Earth crust which form a solid solution, by underground mining exploitation.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.