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386 Advanced Mine Ventilation

23.1.5 Temperatures of Explosions

A general equation for a reliable estimate of flame temperatures for a combustible/
explosive mixture can be obtained as follows. Assume the gas mixture to be 5%
methane in air. For a lower limit mixture like this, the reaction for complete combus-
tion can be written as

0:05 CH 4 þ 0:20 O 2 þ 0:75 N 2 /
(23.7)
0:05 CO 2 þ 0:10 H 2 O ðgasÞþ 0:10 O 2 þ 0:75 N 2

The heat of combustion (reaction) DH is derived from standard heat of formation,
H f , at 298K.

DH 298 ¼ SnDH fn ðproductsÞ SnDH f ðreactantsÞ

Hence,

DH 298 DH 298
DTðproductsÞ¼ ¼ (23.8)
SnC p ðproductsÞ C p mixture

where C p is the specific heat at constant pressure.

C p ; mixture ¼ 0:05 C p ðCO 2 Þþ 0:10 C p ðH 2 OÞþ 0:10 C p ðO 2 Þþ 0:75 C p ðN 2 Þ
(23.9)

The upper limit, T L , for flame temperature for a mixture being discussed can be
calculated by assuming DH 298 for most CeHeOeN combustibles to be 10e11 k
cal per mole of mixture and C p for their products at about 8 10 3 k cal/mol K.
The upper limit of T L is about 1300 C, but significant variations from this value can

occur with very high or very low reactivity [5].
The temperature rise for a constant volume combustion is, similarly, given by

DS 298
DTðproductsÞ¼ (23.10)
C V ðmixtureÞ

where DS 298 is constant volume heat release and C V is average heat capacity for
constant volume.
These temperature rises tend to be 20% higher than those for constant pressure as
shown in Eq. (23.8).

23.1.6 Pressure Rise in Explosions
The pressure rise in an explosion of gas mixture is considered under two categories: (1)
deflagration (subsonic propagation) and (2) detonation (supersonic propagation).