Page 275 - Fundamentals of Enhanced Oil and Gas Recovery

Enhanced Gas Recovery Techniques From Coalbed Methane Reservoirs 263

Peng Robinson model is one of the commonly used models for gas.
Gas viscosity is also pressure and composition dependent. Lorentz Bray Clark
model is a typical model to relate gas viscosity to the composition and pressure [110].

! 4
5
0 24 X i21
μ 2 μ ξ 1 10 5 a i b (8.39)
r
i51
0
where a i is a constant, ξ and μ are the functions of composition of gas, molecular
weights, critical temperature and pressure, and b r represents the reduced molar density.

8.5.2.1.6 Porosity Model
The porosity of cleats and correspondingly permeability change with the alteration of
pressure and/or the amount of adsorbed gas (which results in shrinkage or swelling).
Palmer Mansoori model is among the most popular models used to take this phe-
nomenon into consideration [31].
φ c m 1 K 2 1 Δε

φ 0 5 1 1 φ c0 ð p 2 p 0 Þ 1 φ c0 M (8.40)

where φ is the initial porosity at pressure p 0 , K and M represent bulk modulus and
0
axial modulus, respectively, and Δε represents the total volumetric strain calculated
using the following equation:

N c 21 N c 21
k
k
X ε k β a k p X ε k β a k p 0
Δε 5 2 (8.41)
1 1 P N c β a j p 1 1 P N c
j
k51 j51 j k51 j51 β a j p 0
where β and ε k are matching parameters, and a k and c m are calculated as follows:
k
V k
(8.42)
N c
a k 5 P
j51 V j

1 K
c m 5 2 1 f 2 1 γ (8.43)
M M
where γ is grain compressibility, and f is a fraction ranging between 0 and 1.
The cleat permeability is typically proportional to the cube of cleat porosity
[2,20,75,82,87]. Incorporating all the mentioned equations, the number of unknowns
and equations will be the same. Using numerical methods, e.g., finite volume with a
backward Euler, the resulted PDEs can be solved.