Gas emission into the excavated space during the mining of coal seams

Abstract

We represent a coal seam as a cracked and porous medium in which gas is found in the free and sorbed state. The coal has zero permeability before the seam is mined. As a result of mining of a coal deposit the equilibrium state of the medium is destroyed. This leads to a redistribution of the stress and strain fields in the part of the coal seam near the face, as a result of which a region of nonzero permeability (0, 1.) forms near the face. In this region a nonsteady filtration of gas into the excavated space occurs as a result of the pressure gradient. This region is finite and is determined by the physico-mechanical properties of the coal and the drift, the depth at which the seam lies, and the technology by which it is mined. Because the drift is impermeable, we can with sufficient precision regard the motion of the gas as one-dimensional and use the following equation to describe the process of nonsteady filtration: 02p2/Ox 2 = #/k[m + abRrTo/(1 + ap)2]p-lOp2/Ot 2.(1) where p and # axe the pressure and viscosity of the gas respectively; m is the porosity of the coal; k is the coefficient of permeability; a and b are the sorption constants, determined for hard coals from the isotherms of the sorption of methane, obtained experimentally or approximated by computational methods; Rr is the gas constant; and To is the absolute temperature of the seam.The relation between the filtration velocity v and the pressure of the gas is subject to the D'Arcy law:We shall assume that at the time when the coal seam is exposed an unknown boundary l appears on which the pressure of the gas equals the initial pressure, and that this boundary moves toward the end of the filtration region l..The boundary and initial conditions corresponding to the filtration of gas into the region (0, l) when the unknown moving boundary l has not reached the value l. have the form p(O,t) = v), p(l,t) = p~, p(~, o) = px.Here p0 and Pl are the pressure of the gas on the exposed surface and in the untouched coal massif respectively. To determine the unknown boundary I we form the following kinematic and initial conditions:We introduce the function ~(p) = [m + abRrTo/(1 + ap)~lp-1.