Page 56 - Advanced Mine Ventilation

Turbulent Dispersion of Pollutants in Mine Airways 39

Q
By plotting the experimental data on semilog paper with as the ordinate and
4psc
(s e x) as the abscissa, a straight line with gradient u=2ε r and intercept l n ε r is ob-
tained. In addition to the determination of the radial coefficient of turbulent
dispersion, the model described by Eq. (3.5) can be used to predict concentra-
tions around and at other strategic locations downstream from these continuous
sources.

3.5 Dispersion of Respirable Dust From a Heading

A problem of considerable importance in mines is the dispersion of respirable dust
from a heading being driven with continuous miners. Respirable dust particles are
generally smaller than 10 mm in diameter and behave as a gas. In order that concentra-
tions of respirable dust do not exceed the specified health standards, adequate ventila-
tion must be provided. Eq. (3.1) is modified in this case with the following
assumptions:

1. Cutting or loading machines at the heading virtually occupy the entire width. Consequently,
symmetry in the direction of width can be assumed.
2. Because of obstructions and the narrow height of headings, a symmetry in the direction of
height is also obtained.
3. The concentration of respirable dust is so small that there is no change in air density.
4. The velocity in the direction of the length of the heading is constant.
5. The decay coefficient for respirable dust is a constant. Generally it is a factor of velocity of air
and friction factor of the roadway. Mathematical derivations of this constant are given by
Beal [11].
On the basis of these assumptions, the model for the dispersion of respirable dust
particles is as follows:

2
vc v c vc
¼ ε x 2 u lc (3.8)
vt vx vx
Typical boundary and initial conditions for this case are

1: c ¼ c o at x ¼ 0 )
t > 0
2: c ¼ 0 at x ¼ N
3. c ¼ 0 at t ¼ 0 for all x except at x ¼ 0

Eq. (3.8) is readily solved using the Laplace transform as given below:

2 3
0:5 x p ffiffiffiffiffi
e xða=ε x Þ erfc p ffiffiffiffiffiffi at
2 ε x t
6 7
c o 6 7
cðx; tÞ¼ e ux=2ε x6 7 (3.9)
2 6 p 7
4 xða=ε x Þ 0:5 x ffiffiffiffiffi 5
þe erfc p ffiffiffiffiffiffi þ at
2 ε x t