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Influence of barometric-pressure variation on methane concentration in air flow from longwal region |
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Influence of barometric-pressure variation on methane concentration in air flow from longwal region with adjacent goaf - a mathematical model and calculation algorithm Author A. Krach
The paper presents a manner of such modification of the computer program VentZroby, which was developed at IMG PAN and has served a purpose of predicting the distribution of air and distribution of methane concentration in a mine ventilation network with the goaf, that it includes in the forecast the influence of barometric-pressure variation on methane concentration in a mine ventilation network due to so called goaf respiration. The problem was considered by numerous research workers, let us mention W. Trutwin (1973), St. Wasilewski (1998) and Z. Kajdasz with co-authors (2002). Trutwin (1973) proposed a model of the goaf being one large volume, separated by a filtration zone from an adjacent working. Such a model only aproximately represents the real goaf that is an object with distributed constants and is characterized by spatial distribution of filtration felocity of an air - methane mixture and distribution of methane inflow. These features are taken into consideration by a model of the goaf in the shape of a network of mutualy perpendicular branches (Fig. 1) with methane inflow at nodes (Dziurzyński 1998;Nawrat 1999), which was applied to the computer program VentZroby. In Chapter 2, theoretical background of this model is presented in short: an equation of flow trough a branch of a ventilation network (1), an equation of filtration flow trough the goaf (3), an equation of flow trough a branch of a network that models the goaf (6), and a formula for methane concentration in streams that flow out of a given node of a network of branches (2). The modification of the presented model with the purpose of taking into account the influence of barometric-pressure variation on the distribution of methane concentration in the goaf and branches of a ventilation network is revealed in Chapter 3. Based on the gas law for a binary mixture (7), a formula was derived for dependence of mass flow of an air - methane mixture that flows into the given volume on the speed of pressure and concentration variations in this volume (11). Subsequently, from the mass-balance equation for an air - methane mixture (12) a differential equation (14) was derived that describes the methane-concentration variation in the volume under discusion. The derived equations enabled us to supplement the goaf model, as it was shown on Fig. 2 and 3. On these grounds it is possible to modify the algorithm for numerical calculation of distribution of gases and distribution of methane concentration in branches of a ventilation network ; and branches of the goaf-modeling network in the way which is given in Chapter 4. For succesive time steps a sequence of operation is run, starting from storing the pressure values at the network nodes and calculating the pressure at the nodes for successive pressure value at the outset. Afterwards, new pressures at nodes are calculated trough the relation (16), for these pressures additional mass inflows to the nodes are calculated (17), they are added to the methane mass streams that flow up to the nodes (18), and for these values of the inflows, the distribution of air in branches of the ventilation network is deterrmined, together with branches of networks that model the goaf. For the calculated distributions of air, nodal pressures and distance of the vectors of these pressures from the vectors of the pressures from the relation (16) are determined. Such a sequence of operations is repeated up to a distance of pressure vectors which is smaller than the distance accepted as measure of calculation accuracy. Next, methane concentrations in elementary volumes of the goaf associated with the nodes are determined through numerical solution of the system of differential equations (19) and the whole procedure is repeated for the subsequent time step. Realisation of the presented algorithm requires development of a number of procedures for the computer program and next building it in a proper place of the current version of the VentZroby program. A forecast of distribution of methane concentration in the goaf and branches of a ventilation network, prepared owing to modeling of the ventilation network of a selected exemplary mine through the modified VentZroby program and simulation of barometric-pressure variation, will prove correctness and usefulness of the development of the goaf model in the program.
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2011