Calculation of the motions of gas in a coal seam with a quasilinear law of filtration

Abstract

Problems involving degassing of coal seams are, of course, very important. Most research on the processes involved has been based on equations proposed to represent isothermal gas filtration [i] in which Darcy's law holds.The gas permeability is regarded as a characteristic of the medium, independent of the filtration conditions, in particular, of the gas filtration parameters and the state of stress of the rock.Under real conditions all these characteristics, and to a great extent the mechanical load on the filtering coal seam, have a marked influence on the gas permeability.As a result, the coefficient of gas permeability obtained for filtration of a particular gas under some pressure in the absence of mechanical actions on the coal may have only a limited range of applicability.Thus, consideration of the state of stress of the rock leads us to reject the linear law of filtration.Nikolaevskii et al. [2] give a closed system of equations (based on experimental data on the gas permeability and the porosity as functions of pressure) in the filtration approximation in which account is taken of the deformations occurring in the porous collectors.Khodot [3] describes experiments to determine the porosity and gas permeability in relation to the fluid pressure in the pore of a coal seam.A class of exact solutions of the equations of motion of a ga s in a deformed coal seam was derived by us in [4].In this article, using as examples two typical problems concerning the gas flow in a borehole allowing for the state of stress of the seam, we will investigate the problems involved.Let us consider the steady isothermal filtration of gas in a degassing borehole. The equation for the motion of the fluid in a one-dimensional coal mass, involving desorption phenomena, iswhere m = m(p) is the porosity, a and b are Langmuir's sorptio n constants, R is the universal gas constant, T is the temperature, p is the gas pressure, ~ = l(p) is the coefficient of gas permeability; u = 0 in the plane case, and ~ = 1 in the axisymmetric case. Here ~in is some initial permeability of the coal seam, Po is the gas pressure in the undisturbed massif, and ~ and 8 are empirical constants.Problem i. Consider a one-dimensional coal seam of length 2Z bounded at either end by impermeable rocks.To reduce the gas pressure in it we bore a hole in which aInstitute of Mining, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk.

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“…The simplest model is a macro model ( Figure 1) with a homogeneous structure (Vorozhtsov et al, 1975;Jones et al, 1982) that describes the process of sorption as a process requiring no time, so it can be used only for forecasting trends. This macro model possesses a statistically homogeneous convectiveconductive flow field (macro system).…”

Interaction of Cleat-Matrix on Coal Permeability from Experimental Observations and Numerical Analysis

“…This means that interconnected pores of the coal matrix is well developed. The gas-bearing coal matrix provides a mass source term for the gas flow equation [11] via gas adsorption/desorption. This assumption ignores the gas supply hysteresis effect from the matrix blocks and consequently underestimates coal permeability (ii) The nonequilibrium and pseudosteady state assumption is that a time-dependent gas transfer is driven by pore pressure gradient between the coal matrix and the cleat [12].…”