Page 263 - Fundamentals of Enhanced Oil and Gas Recovery
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Enhanced Gas Recovery Techniques From Coalbed Methane Reservoirs 251
The total amount of gas uptake/desorption of both micro/macropores is calculated
as follows:
M t M at 1 M it M at M it
5 5 1 2 αÞ 1 α (8.19)
ð
M N M aN 1 M iN M aN M iN
where α is M iN = M aN 1 M iN Þ :
ð
Although bidisperse model fits the data more accurately compared to unipore
model, due to a greater number of fitting variables, it yet does not include the whole
range of pore sizes.
8.4.2.3 Pseudo Steady State Model
Another model to describe gas diffusion behavior in coals is pseudo steady state
model. This model describes gas diffusion in coal matrix as follows [60,61]:
dM ½ M N 2 M t
52 (8.20)
dt t 0
where t 0 is a time constant indicating the required time for adsorption/desorption of
63.2% of the total amount of gas at equilibrium condition. This equation, when sepa-
rating the variables and integrating both sides, would be rewritten as
dM dt
ð ð t
M t
5 2 (8.21)
0 ½ M N 2 M t 0 t 0
The solution of Eq. (8.21) results in
M t t
5 1 2 exp 2 (8.22)
M N t 0
This explicit equation suggests that adsorption/desorption amount of a gas in coals
is exponentially correlated to time.
Furthermore, an experimental fitting parameter, β, was added to Eq. (8.22) to get
more accurate history match results [53,54,62]:
" #
β
t
M t
5 1 2 exp 2 (8.23)
M N t 0
While this parameter is aimed at describing the spread in sorption times, the vari-
able β varies between 0 and 1 based on coal characteristics. Drawing a comparison
among unipore, bidisperse, and exponential models reveals that the kinetics phenom-
ena of gas diffusion in coal, during adsorption/desorption process, is more accurately
described by exponential model [Eq. (8.23)] than unipore and bidisperse models
[53,54].
