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Mathematical model of methane caused by a collapse of rock mass crump |
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Mathematical model of methane caused by a collapse of rock mass crump Authors: W. Dziurzyński, A. Krach
Rock mass collapses in mines containing gas are accompanied by an intensive outtow or discharge of methane. Movement of this gas through the ventilation network results in disturbances of the methane concentration distribution in sectors of the mine ventilation network and may lead to an explosion hazard. This article presents a mathematical model of methane emission following a collapse. It discusses the mechanics of the phenomenon of collapse and its gas dynamics. Two key sources of methane emission have been idcntified: release of gas from fragments of side wall rocks transported in to the working, filtration inflow of gas to the working through the stress-relieved zone formed as a result of the rheological process and the rock mass beyond that zone. For the methane release from coal fragments the four-component emission model proposed by Airuni (1987) has been used, which includes methane emission from the volume of sorbed particles, the surface of these particles, supersorbed particles and filtration-sorbed particles. The paper presents parameters of individual components of thc emission. It has been demonstrated that the last component with the highest time constant has a significantly larger share in the total gas absorbability than components with lower time constants. For the gas intfow from the stress-relieved zone and the rock mass the filtration flow model has been adopted (Tarasow, Kolmakow 1978), which includes the depth of the stress relieving zone variable in time, the porosity coefficient and permeability coefficient as a function of porosity and gas pressure. On the basis of this model and with the use of results of experimental research of changes in the rate of gas release during the formation of the stress-relieved zone, the initial velocity of methane release has been approximated by the exponential function. By adding both sources of methane emission, the total stream of gas volume tlowing to the working in the collapse zone was calculated in relation to a length unit of the working. The presented model of methane emission following a rock mass tremor or collapse and the formulation of the mathematical model of the air and methane mixture distribution in the mine ventilation network will allow for developing professional software simulating the aforementioned phenomena.
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2009