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232 Advanced Mine Ventilation

Figure 14.3 Gas isotherms for US coal seams.

It is to be noted that high-rank (low-volatile bituminous) coals contain more gas
than the low-rank (high-volatile bituminous) coals (HVA, HVB, HVC) at the same
confining pressure. It is also clear that the sorption capacity of all coal increases
with pressure, but the increase occurs at an ever-decreasing rate as the sorption capac-
ity reaches an asymptotic limitdthe saturation limit.
A mathematical representation for these isotherms was given by Langmuir [11] and
is expressed as

bP
V ¼ V m (14.4)
1 þ bP
3
where V is the volume of gas contained at pressure P, ft /t; V m is the maximum
3
sorption capacity of coal, ft /t; P is the pressure, psi; and b is the Langmuir
constant, psi. 1
For indirect determination of the gas content of coal at a given pressure, Eq. (14.4)
can be rewritten as

P P 1
¼ þ (14.5)
V V m bV m