Page 192 - Advanced Mine Ventilation

172 Advanced Mine Ventilation

In this case, the exhaust emissions are free to disperse on either side of the diesel
engine. The differential equation now becomes

2
vc q vc v c
þ ¼ E x (11.16)
vt 2F vx v 2
x
And the boundary and initial conditions are obtained exactly as in the case of Eq.
(11.13). They are

q vc q
c j x¼0 E x F ¼ c i for t > 0 (11.17)
2 vx 2
x¼0
c/0as x/N for t > 0 (11.18)

c ¼ 0at t ¼ 0; x > 0 (11.19)

The physical meaning of these equations is the same as in the previous case. The
solution of Eq. (11.16) with the given boundary and initial conditions is obtained
q
by substituting for V r in Eq. (11.13) and dividing the right-hand side by 2 and is
2F
given below:
⎡ qt ⎤
⎢ x − 2F ⎛ qx q t ⎞ 2 qx ⎥
⎢ erfc − ⎜ 1+ 2E F + 4F E ⎟ exp 2E F erfc ⎥
2
x
c ⎢ 2E t ⎝ x x ⎠ x ⎥
c = i ⎢ 2 ⎥ (11.20)
2 ⎢ x+ qt 1/2 ⎛ x − qt ⎞ ⎥
⎢ 2F + q ⎛ t ⎞ exp − ⎜ 2F ⎟ ⎥
⎜
⎢ 2E t FE π ⎜ ⎟ 2 E t ⎟ ⎥
⎝
x ⎠
x ⎟
⎢ ⎣ x ⎜ ⎝ ⎠ ⎥ ⎦

11.4.3 Multiple Diesel Engines in a Single Roadway
The case of multiple diesel engines in a single roadway is a natural outgrowth of the
case of a single engine in a single roadway. Typical mining situations with exhaust
type ventilation are shown in Figs. 11.4 and 11.5.
Fig. 11.4A shows the layout for the drivage of a long tunnel, whereas Fig. 11.4B
represents a long entry. Fig. 11.4C is a simplified representation of an actual mining
layout shown in Fig. 11.5. The length of haul in Fig. 11.5 is only 500 ft but the real
advantage of diesel engine deployment in coal mines will accrue if this length could
be increased to cover the entire panel length, which is typically 5000e10,000 ft. In
that case, more than one diesel engine will be needed to insure a continuous removal
of coal from the working face. Generally, diesel engines move faster than the air cur-
rent in the face area and consequently, the air flowing in the haulage roadway will be