Page 71 - Advanced Mine Ventilation

54 Advanced Mine Ventilation

where Ex is the longitudinal coefficient of turbulent dispersion; u(x) ¼ u o exp( ax),
where u(x) is the air velocity at any point on the face; u o is the velocity of air at head
gate; a is a leakage coefficient that is experimentally determined; q(x) is the methane
source and includes both the steady and transient methane emissions; p(x) is the loss of
methane in the gob at any point on the face due to air leakage; c is the concentration
of methane at a “small element” of longwall face, defined as Q/V where Q is the total
methane emission; V is the volume of air at the same location.
Boundary conditions are
At x ¼ 0 (i.e., the head gate); dc/dx ¼ 0, i.e., methane concentration is a constant.
At x ¼ L (i.e., the tail gate) c ¼ 0.01 (or any other statutory limit).
Eq. (4.3) is a second-order, nonhomogenous differential equation, and no analytical
solution can be obtained in a closed form. However, solutions can be obtained using
finite difference or finite element techniques and computers. The second challenge
here is to accurately measure values of Ex; q(x) and p(x).
The minimum quantity of air thus calculated must be increased by at least 25% to
provide some cushion for peak emissions. If this quantity of air cannot be delivered to
the tail gate of a longwall face owing to airway size and number (usually three) and the
fan size, the width of the longwall panel must be reduced. In moderately gassy mines
of the northern Appalachian Basin of the United States, gas emissions on the longwall
face limit the width of the panel from 1200 to 1300 ft [8].

4.7 Limitations on the Longwall Face Width Owing to
Gob Methane Emissions

In each basin, the coal seams have two emission characteristics. They are as follows:
1. Specific emission of the coal seam
2. Specific gob emissions for the coal seam

4.7.1 Specific Emission of a Coal Seam
It is the amount of gas produced by a section of 100 ft of a horizontal borehole drilled
into the coal seam. It ranges from 3 to 25 MCFD/100 ft depending on the rank, perme-
ability, and depth of the coal seam [1]. More on it will be discussed later in Section 4.3.

4.7.2 Specific Gob Emissions for the Coal Seam

As shown in Fig. 4.2, when a coal seam is mined out by a longwall face, the strata
above and below get fractured and begin to produce gas. For each basin, it is a char-
acteristic of the coal seam. For example, the Pocahontas #3 coal seam in the Central
Appalachian Basin, United States, produces 30 MMCF/acres of the gob.