Page 261 - Fundamentals of Enhanced Oil and Gas Recovery

Enhanced Gas Recovery Techniques From Coalbed Methane Reservoirs 249

where V j is the gas content of component j, V Lj is the Langmuir volume constant of
component j, p Lj is the Langmuir pressure constant of component j, y j is the free gas
mole fraction of component j, and p is the reservoir pressure.
It should be noted that in gas reserve estimation of a coal, the total amount of free
gas, dissolved gas in water, and adsorbed gas should be considered to prevent any
reserve underestimation.

Example 8.2: San Juan Basin (Fruitland coal)—methane content estimation using
extended Langmuir equation.
Arri et al. provided sorption characteristics of Fruitland formation for some gases
including CO 2 and methane [48]. The Langmuir pressures for these two gases are
204.5 psia and 362.3 psia, respectively. Additionally, the Langmuir volume constant of
CO 2 and methane were estimated at 1350.1 scf/ton and 908.4 scf/ton. Assuming the
coal entails 90% mole fraction methane and 10% CO 2 , at 800 psia the methane con-
tent of coal is calculated using Eq. (8.14)

ð 800 3 0:9Þ=362:3
V methane 5 908:4 3
1 1 800 3 0:9Þ=362:3 1 800 3 0:1Þ=204:5
ð
ð
Therefore, in such reservoir condition, there is 534.3 scf of methane per each ton
of the coal rock.

8.4.2 Diffusion

Subsequent to desorption from internal coal surfaces, the gas diffuses through matrix
and micropores to reach cleats. Therefore, gas diffusion in coal matrix system is the
second step in gas movement, for describing its mechanism that some models have
been suggested.

8.4.2.1 Unipore Model
One of the earliest models presented to describe the gas diffusion behavior in coal
matrix is unipore diffusion model. This model has been developed based on the Fick’s
second law with the assumption of a spherical symmetric flow [44,49]. The unipore
model, Eq. (8.15), assumes that microspores in coal are monosized; whereas, in prac-
tice, coal matrix has a variety of pore sizes. Therefore, the unipore model is accurate
only for coals with homogenous pore structure.

2
@C @ C 2 @C
5 D 1 (8.15)
@t @r 2 r @r