Page 58 - Advanced Mine Ventilation

Turbulent Dispersion of Pollutants in Mine Airways 41

3.7 Concentration Growth in a Roadway With Uniformly
Distributed Source

When a heading is being driven in a coal mine or any other gas-bearing strata, it
is important to know the maximum concentration that can build up at the face.
In coal mines, an exhaust-type ventilation is usually employed to keep dust and
gas concentrations low. Because of this, gases given out by the walls of the
heading are carried to the face, and there is a gradual rise in gas concentration
from the outbye end to the inbye end of the heading. A mathematical model for
this situation is

2
v c vc
ε x 2 þ u q ¼ 0 (3.14)
vx vx
where q is the uniformly distributed source for gases from walls of the roadway.
Assuming the boundary conditions as:

vc
¼ 0at x ¼ 0
vx
and

vc
ε x þ ucj x¼L ¼ qL
vx
x ¼ L
where L is the length of the roadway, a solution of Eq. (3.14) is obtained as below:
q h ε x i
cðxÞ¼ x 1 e ux=ε x (3.15)
u u
substituting for c, the maximum permissible value, the quantity of diluent air can be
obtained from Eq. (3.15).The derivation of ex is discussed in detail in Chapter 11 of the
book.

Problems

3.1 Using Eq. (3.4), calculate 3 x
3
If Q ¼ 1ft of SF 6 (sulfur hexachloride)
A ¼ 100 ft 2
u ¼ 200 ft/min
t ¼ 20 min
x ¼ 10,000 ft
c(x,t) ¼ 5 ppm by volume (5 parts of 1 million).
3.2 Assume the above experiment is done in a tunnel of 10 feet diameter, and the source is
3
continuous at 0.1 ft /min. Use Eq. (3.7) to determine 3 x .
Airflow remains the same at 20,000 CFM.