Solution to the problems of gas movement in coal seams with nonlinear filtration laws
During coal mining operations, the explosive gas methane is liberated from the face, and as the mining operations are intensified, gas bursts arise. These factors reduce the rate of working coal deposits. Among existing methods of preventing these undesirable phenomena, one of the most important is preliminary degassing of the worked section. For this purpose, the coal is drained via a number of boreholes, or working of one face is stopped for a while. Since the structure of the seam is disturbed by mining operations, gas starts to filter in the seam toward regions of reduced pressure. Equations representing the motion of gas in coal seams during isothermal desorption were derived by Krichevskii. This class of problems in the nonlinear theory of filtration was later studied by Molokovich and others, who used the methods of separation of variables, integral transformations, and straight lines without investigating the mathematical questions of the solvability of the problem and the stability of the solution. The method of Bergman and Nazarov permitted the construction of a solution to this class of problems for substantially any type of filtration law with natural physical properties at the stopping point and at an infinitely remote point in the plane. In this article we discuss the solution to the problems by the methods of straight lines and of Bergman and Nazarov when the imaging of the flow region from the (x,y) plane to the (v,theta) image plane leads to unbounded regions with cuts, projections, etc. We show that the numerical solution based on the method of straight lines is convergent, and we investigate the influence of the type of nonlinear filtration law on the kinematic characteristics of the flow. We show that in solving problems of these two classes we can successfully make use of the method of approximation of the filtration law, by analogy with the methods developed in gasdynamics.
- Research Organization:
- Inst. of Mining, Novosibirsk, USSR
- OSTI ID:
- 6172285
- Journal Information:
- Sov. Min. Sci. (Engl. Transl.); (United States), Vol. 14:1; Other Information: Translated from Fiz.-Tekh. Probl. Razrab. Polezn. Iskop.; No. 1, 52-62(Jan 1978)
- Country of Publication:
- United States
- Language:
- English
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