Page 274 - Fundamentals of Enhanced Oil and Gas Recovery

262 Alireza Keshavarz et al.

where K is the permeability tensor, k rl is the relative permeability of phase l which is
a function of saturation, ρ is the density of phase l, μ is the viscosity of phase l, and g
l l
is the directional gravity acceleration.
The two pressures can be related to each other through capillary pressure (p c ) that
is in turn a function of saturation.

p g 2 p w 5 p c (8.35)

8.5.2.1.3 Fick’s Law
Using Fick’s law, molar flux rate ~ j will be related to the partial pressure (concentra-
l
tion) gradient between cleats and matrix:
ð
~ j i ~ndA D i σ C i 2 V i ρ Ω (8.36)

coal
@Ω
where V i ρ coal is the maximum molar density in matrix which is obtained in equilib-
rium condition corresponding to the partial pressure of component i at the cleats. V i
is calculated using a sorption model, ρ coal is coal density, and D i is the diffusion coeffi-
cient corresponding to component i. σ is the matrix cleats interface area
[Eq. (8.25)].

8.5.2.1.4 Sorption Model
As discussed in the sorption section [Eq. (8.14)], extended Langmuir model is a
and coal characteristics
widely used equation for relating V i to partial pressure p g y i g
).
(V Li and p L i
8.5.2.1.5 Equation of State
Using equation of states, molar densities and viscosities can be related to partial pres-
sure. Water viscosity is normally assumed constant. Water molar density is related to
pressure using the compressibility factor (c w ) that can be assumed constant for water
0
ð
e c w p w 2p Þ (8.37)
b w 5 b w0
0
is the molar density at a reference pressure (p ).
where b w0
b g can be related to pressure and gas composition using gas law.
p g
b g 5 (8.38)
zRT
where R is the gas constant, T is the temperature, and z is the gas compressibility that
is a function of critical temperature and pressure.