Page 251 - Fundamentals of Enhanced Oil and Gas Recovery

Enhanced Gas Recovery Techniques From Coalbed Methane Reservoirs 239

Coal permeability, similar to other reservoirs, is dependent on the effective stress onto
the reservoir that is a function of reservoir depth and pressure differential. However,
unique to coals, the gas desorption process is also influential in determination of the
permeability value of the reservoir at any given time. In fact, these two effects function
competitively. The effective stress increase due to the reservoir pressure drawdown obvi-
ously imposes an adverse effect on the cleat permeability through narrowing the fissures.
On the other hand, the gas desorption as a response to reservoir pressure drawdown
causes the reservoir matrix to shrink, thereby increasing the cleat permeability.
Consequently, the interaction of these two phenomena governs the shape of the cleat
system and determines permeability value at any given condition [32].
The outcome of this interaction might increase the permeability value up to 100
times, being the case in San Juan basin, USA. This occurrence is in a sharp contrast
with conventional reservoirs in which the reservoir depletion leads to a decrease in
absolute permeability [33]. In bituminous coals, the typical porosity is around 1%, and
99% of the reservoir volume is accounted for by matrix [2]. Under such condition,
given the cubic relationship between permeability and porosity, an increase in cleat
porosity from 1% to 2% in response to reservoir depletion and corresponding matrix
shrinkage would result in an eightfold rise in permeability value of the reservoir. It
goes without saying that for lower rank coals, in which the initial porosity is far more
than 1%, the same increase in porosity (1%) results in smaller increase in permeability
measure. Therefore, matrix shrinkage has a more significant effect on permeability
measure in high-rank coals. Moreover, apart from the positive matrix-shrinkage effect
on cleat absolute permeability, such phenomenon favors the relative permeability to
gas, because for the same amount of water inside the cleats, an increase in porosity
lowers the water saturation percentage.
There has been some models presented to describe the behavior of coal permeabil-
ity with respect to the effect of mentioned influential factors on this parameter within
the reservoir depletion. One of the most widely used permeability models, which is
based on the cubic relationship of permeability and porosity, was suggested by Palmer
and Mansoori and is shown below after solving for the axial modulus and the relation-
ship between axial and bulk modulus [34]:
φ ð1 1 νÞð1 2 2νÞ c o 2ð1 2 2νÞ p i p
φ i 5 1 1 ð1 2 νÞEφ i ðp 2 p i Þ 1 φ 3ð1 2 νÞ p i 1 p l 2 p 1 p l (8.3)
i
where ν is the Poisson ratio, E is the Young modulus, p is the pressure at any given
time, p i is the initial pressure, c o is the volumetric strain coefficient, and p l is the
Langmuir pressure.
The second term on the right-hand side of the equation represents the effects of
stress on the porosity, and the third term illustrates how porosity is affected by matrix
shrinkage. While during natural depletion, the third term of this equation is always