Page 252 - Fundamentals of Enhanced Oil and Gas Recovery

240 Alireza Keshavarz et al.

positive because gas desorption causes the matrix to shrink, the second term is nega-
tive since the depletion increases the effective stress, and this phenomenon in turn
attempts to lower the cleats’ width, thereby reducing porosity and permeability.
Depending upon the mechanical characteristics and also sorption properties of the
rock, either of the two terms might dominate. It should be noted that for ECBM
recovery, in which the effective stress decreases with the injection pressure, and matrix
swelling is the expected phenomenon rather than matrix shrinkage, the two terms of
the above equation function much differently. It will be discussed in detail in the
ECBM section.

Example 8.1: San Juan Basin (Fruitland coal)—permeability estimation using Palmer
and Mansoori model.
Mavor and Vaughn in 1998 presented some required properties of Fruitland coal
located in San Juan Basin for calculating the coal permeability, taking into account the
matrix shrinkage as well as stress-related effects [34]. The well VC 32-1 had an aver-
age pressure of 956.7 psia in November 1990, which reduced to 527 psia through
depletion by October 1994. The volumetric strain was 0.01266 and the initial poros-
ity stood at 0.000457. Young’s modulus, Langmuir pressure, and Poisson’s ratio of the
rock amounted at 521,000 psi, 368.5 psia, and 0.21, respectively.

Substituting the given measures in Eq. (8.3):
φ
φ i 5 1:22

It means that the porosity measure of the rock has been enhanced by 0.22 during
the pressure drawdown. Considering the initial absolute permeability of 17.2 mD in
Eq. (8.2):
φ
k 3 3
5 5 ð1:22Þ
17:2 φ i
Therefore, the permeability value of the mentioned coal would be 31.2 mD at
527 psia according to Palmer and Mansoori model.
A couple of years later than the Palmer and Mansoori model, Shi and Durucan
introduced a dynamic model for predicting the permeability changes taking into
account the effects of stress and matrix shrinkage during the natural depletion of coals
[27]. The permeability ratio in this model is exponentially related to the changes in
effective horizontal stress normal to the cleats, as observed in Eq. (8.5).
ν Eε l p p 0
σ 2 σ 0 52 ðp 2 p 0 Þ 1 2 (8.4)
1 2 ν 3ð1 2 νÞ p 1 P ε p 0 1 P ε