Joint probability distribution of methane currents in a system of faces working a group of seams
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PROBABILITY
DISTRIBUTION
IN A S Y S T E M O F F A C E S W O R K I N G
OF M E T H A N E
CURRENTS
A GROUP OF SEAMS
S. A. K a r i m a n
UDC 622.272:519
Operation o f automatic control systems for production processes in coal pits leads to the necessity of creating adequate mathematical models of the processes accompanying coal winning. For example, the efficiency o f an automatic control system for ventilation o f the extraction operations depends on how far we can correctly represent the dependence o f the rate of gas emission in the extraction faces on the actual loads on them at any time. The tendency towards mechanization of extraction operations which has appeared in the last decade is leading not only to an increase in the loads on the faces, but also to an increase in their nonuniformity. We have processed actual data from seven faces of the "Polysaevskaya-2" pit (Kuzbass), four faces of the "Oktyabr'skaya" pit, eight faces of the No. 21 Sh/~ pit (Donbass) and 12 faces of pits 39-40, Zubovskaya No. 4, and Lipkovskaya No. 6 (Moscow coalfield): we found that the dispersions of the output Aj(t) in time t and their mutual correlation moments can be represented by linear functions of time, KAj(t)At(t ) : grit;
l, ]-----1, 2, . . . ,
(1)
where the dispersion coefficient rapidly rims with increase in the mean load on the face. This shows that in working faces with a large load (in practice, one above 300-500 tons/day), it is extremely important to take account of nonuniformity of the output at different times. Neglect of this will lead to a complete discrepancy with reality. This also applies to analysis of the flow of methane from the coal near the face into the atmosphere of the face area. The relation between the rate of gas emission from a single part of the surface of the coal seam (q) and the time of its exposure is fairly well approximated by an exponential function, q (0) --- qle-;~
(2)
For a unidirectional scheme of working of the cutting machine in a face of length I fi the total methane flow from the exposed surface of the coal seam into the atmosphere o f the face area can be represented, with the aid of Eq. (2), in the form f
t
Q(t)=.f qtO( )ldx=:,,tf +a f f e-gOt x) d x . o
o
Here x is the distance in meters traveled by the coal cutter from the given section of the seam to a point where it is situated at a time t. The time of exposure of each section of the seam can be represented as a difference,
A. A. Skochinskii Instituteof Mining, Moscow. Translated from Fiziko-Tekhnicheskie Problemy Razrabotld Poleznykh Iskopaemykh, No. 4, pp. 110-11q, July-August. 1974. Original article submitted January 7, 1974.
9 19 75 Plenum Publishing Corporation, 22 7 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy o f this article is available from the publisher
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